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1. Variety (universal Algebra) - Wikipedia, The Free Encyclopedia In universal algebra, a variety of algebras is the class of all algebraic An Equational class for some signature is the collection of all models, http://en.wikipedia.org/wiki/Variety_(universal_algebra)

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Variety (universal algebra) From Wikipedia, the free encyclopedia Jump to: navigation search In universal algebra , a variety of algebras is the class of all algebraic structures of a given signature satisfying a given set of identities . Equivalently, a variety is a class of algebraic structures of the same signature which is closed under the taking of homomorphic images, subalgebras and (direct) products . In the context of category theory , a variety of algebras is usually called a finitary algebraic category A variety of algebras should not be confused with an algebraic variety . Intuitively, a variety of algebras is an equationally defined collection of algebras , while an algebraic variety is an equationally defined collection of elements from a single algebra . The two are named alike by analogy, but they are formally quite distinct and their theories have little in common. Contents Birkhoff's theorem Examples Variety of finite algebras Category theory ... edit Birkhoff's theorem Garrett Birkhoff proved equivalent the two definitions of variety given above, a result of fundamental importance to universal algebra and known as

2. Atlas: Universal Algebra And Lattice Theory (Dedicated To The 70th Birthday Of B universal algebra and Lattice Theory (Dedicated to the 70th birthday of B. Csakany) Stephan Földes On Equational classes of Boolean functions http://atlas-conferences.com/c/a/i/v/01.htm

Atlas home Conferences Abstracts about Atlas Universal Algebra and Lattice Theory (Dedicated to the 70th birthday of B. Csakany) July 22-26, 2002 University of Szeged Szeged, Hungary Organizers Agnes Szendrei, Laszlo Szabo, Miklos Dorman Conference Homepage Abstracts This is an archive of abstracts accepted to this conference. For more listing and sorting options, see the active list. Erhard Aichinger 2-affine complete algebras need not be affine complete. Daciana Alina Alb Tensor products of compact rings Joel Berman Bela Lettres The lattice of projection operators of a subtractibe nearsemilattice Sinisa Crvenkovic On the Berman Conjecture for Finite Semigroups Gabor Czedli Optimal Mal'tsev conditions for modular congruence lattice identities Patrick Dehornoy The geometry monoid of an identity Dejan Delic Endomorphism Monoid of the Random Graph Guenther Eigenthaler Congruence regularity and its generalizations On equational classes of Boolean functions Kazimierz Glazek Independence notions from a general algebraic point of view Martin Goldstern Intervals in clone lattices on infinite sets Miroslav Haviar Standard topological quasi-varieties - examples and problems Csaba Henk Representation Theory of Cylindric Lattices Tolerance intersection property in congruence modular varieties Jaroslav Jezek Membership problems for finite algebras Vinayak V. Joshi

3. JSTOR Universal Algebra. universal algebra, the general theory of algebraic systems, Chapter 4 free algebras, their construction and applications to Equational classes and http://links.jstor.org/sici?sici=0022-4812(197312)38:4<643:UA>2.0.CO;2-S

4. Universal Algebra And Logic We will discuss an approach using the techniques of universal algebra, which has proved most . Title QuasiEquational Classes of Wajsberg algebras. http://www.math.vanderbilt.edu/~ual/semi.html

5. PlanetMath: Equational Class is any class of algebras, then $ HSP(K)$ is an Equational class. logic and foundations Model theory Equational classes, universal algebra) http://planetmath.org/encyclopedia/Subvariety.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About equational class (Definition) Let be a class of algebraic systems of the same type is the class of subalgebras of algebras in is the class of direct products of non-empty collections of algebras in , and is the class of homomorphic images of algebras in It is clear that is a subclass of , and An equational class is a class of algebraic systems such that , and are subclasses of . An equational class is also called a variety A subclass of a variety is called a subvariety of if is a variety itself. Examples In the variety of groups, the classes of abelian groups is equational. However, the following classes are not: simple groups cyclic groups finite groups , and divisible groups In the variety of rings , the classes of commutative rings and Boolean rings are varieties. Most classes of rings, however, are not equational. For example, the class of

6. Nelson (print-only) Defining a class of universal algebras to be algebraic if it is closed under in the lattice of Equational classes of semigroups in algebra universalis, http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Nelson.html

Evelyn Merle Roden Nelson Born: 25 Nov 1943 in Hamilton, Ontario, Canada Died: 1 Aug 1987 in Hamilton, Ontario, Canada Evelyn Nelson 's name before she married was Evelyn Merle Roden. Her parents were Russian immigrants who came to Canada in the 1920s and they were to have a strong influence in encouraging their daughter in her educational pursuits. Although her parents had struggled when they first arrived in Canada, by the time Evelyn was born they were comfortably off running a clothing business. Evelyn attended Westdale High School in Hamilton, Canada, and soon showed that she had quite outstanding gifts but it is very much to her parents credit that they encouraged her talents in science and mathematics although they themselves had little experience of these topics. Bernhard Banaschewski writes [3]:- One of the most positive influences on her life ... was the unwavering reassurance she received from her parents. It was, indeed, not the easiest in those days for a girl to become passionately interested in mathematics and natural science, with many attitudes pervading the schools, and society at large, that were acting as powerful influences against such a choice. Thus it is very much to her parents' credit that they did everything possible to encourage her to follow her natural inclinations and innate talents, no matter how unfamiliar this might have appeared. They took the greatest pride in her scholastic successes ... After graduating from Westdale High School in Hamilton, Evelyn entered the University of Toronto. She had not yet made the decision to concentrate on mathematics and she entered a course of study of mathematics, physics and chemistry. She remained on this course for two years and then made the decision to move back to her home town of Hamilton and to complete her studies at McMaster University. Soon after her return to Hamilton she married Mort Nelson, who was an undergraduate at McMaster and, of course, he was the reason for her move from Toronto.

7. "Mal'cev Varieties" Citations S. Burris and H.P. Sankappanavar, A Course in universal algebra, Springer, J. Hagemann and C. Herrmann, Arithmetical locally Equational classes and http://orion.math.iastate.edu/jdhsmith/math/cytmalvr.htm

Selected citations of "Mal'cev Varieties" J. Hagemann and C. Herrmann, A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity , Arch. Math. (Basel) Universal Algebra (2nd. edition), Springer, New York, NY, 1979. W. Taylor, Equational logic , Houston J. Math., Special Survey Issue, 1979. S. Burris and H.P. Sankappanavar, A Course in Universal Algebra , Springer, New York, NY, 1981. H.P. Gumm, A cancellation theorem for finite algebras , Colloq. Math. Soc. J. Bolyai J. Hagemann and C. Herrmann, Arithmetical locally equational classes and representation of partial functions , Colloq. Math. Soc. J. Bolyai P.T. Johnstone, Stone Spaces , Cambridge University Press, Cambridge, 1982. H.P. Gumm, Geometrical methods in congruence modular algebras , Memoirs of the Amer. Math. Soc. (1983) No. 286. M.R. Vaughan-Lee, Nilpotence in permutable varieties , pp. 293-308 in "Universal Algebra and Lattice Theory" (eds. R.S. Freese and O.C. Garcia), Springer, Berlin, 1983. J. Jezek and T. Kepka, Medial Groupoids , Academia, Prague, 1983.

8. Conditional Terms And Their Applications In Algebra And Boolean constructions in universal algebra , Russian Math. and permutability of congruence relations in Equational classes of algebras , Proc. Amer. http://www.turpion.org/php/reference.phtml?journal_id=rm&paper_id=415&volume=56&

9. Publications Embedding the dual of Pim in the lattice of Equational classes of Proceedings of the 1978 conference on universal algebra in Esztergom, 161 168. http://www.math.uwaterloo.ca/~snburris/htdocs/MYWORKS/publ.html

BOOKS [with R. McKenzie] Decidability and Boolean Representations. Memoirs A.M.S. No. 246, July 1981. [MR [with H.P. Sankappanavar] A Course in Universal Algebra. Graduate Texts in Mathematics No. 78, Springer-Verlag, 1981. [MR The On-Line Millenium Edition Logic for Mathematics and Computer Science. Prentice-Hall, 1998. ISBN 0-13-285974-2 Number Theoretic Density and Logical Limit Laws. Amer. Math. Soc. 2001 ISBN 0-8218-26666-2 PAPERS Representation theorems for closure spaces. Colloq. Math. (1968), 187 - 193. [MR PDF (18.5 Megs) Closure homomorphisms. J. of Algebra (1970), 68 - 71. [MR PDF (15.5 Megs) A note on varieties of unary algebras. Colloq. Math. (1971), 195 - 196. [MR PDF (6 Megs) [with E. Nelson] m in the lattice of equational classes of commutative semigroups. Proc. AMS (1971), 37 - 39. [MR PDF (7.0 Megs) On the structure of the lattice of equational classes . Algebra Universalis (1971), 39 - 45. [MR PDF (10.5 Megs) [with E. Nelson] in the lattice of equational classes of semigroups. Algebra Universalis (1971), 248 - 253. [MR

10. The Max-plus Algebra Of The Natural Numbers Has No Finite Equational Basis 6 6 S. Burris, H.P. Sankappanavar, A Course in universal algebra, Springer, 21 21 R.E. Park, Equational classes of nonassociative ordered algebras, http://portal.acm.org/citation.cfm?id=766741.766751

11. Publikacje universal algebra and quasigroup theory. Papers from the Conference on universal . 5 Romanowska, Anna, On free algebras in some Equational classes http://www.mini.pw.edu.pl/~aroman/publikacje.html

Publikacje naukowe (PUBLICATIONS): Ksi¹¿ki (BOOKS) Heldermann Verlag, Berlin, 1985. xii+158 pp. ISBN: 3-88538-209-1. [08-02 (06A12 20N15)] Errata: http://www.math.iastate.edu/jdhsmith/math/MTerrata.pdf Errata: http://www.math.iastate.edu/jdhsmith/math/PMArrata.pdf Romanowska, Anna B., Smith Jonathan, D. H., Modes, World Scientific, Singapore, 2002, ix+623 pp. ISBN: 981-02-4942-X Errata: http://www.math.iastate.edu/jdhsmith/math/MODErata.pdf Section 5.1 Algebraic language and harmony in the monograph: J. Halu ka, The Mathematical Theory of Tone System, Marcel Dekker, Inc., Ister Science Ltd., New York, Basel, Bratislava, 2003, pp. 75-86. Praca redakcyjna (EDITORIAL WORK) Demonstratio Math. Vol XXIV , No 1-2, (1991) (Papers from the Conference on Universal Algebra, Quasigroups and Related Systems, Jadwisin, 1989). Edited by A. Romanowska and Z. Lonc. Demonstratio Math. Vol. XXVII , No 3-4, (1994) (Volume dedicated to Professor Tadeusz Traczyk). Edited by A. Romanowska. Universal algebra and quasigroup theory. Papers from the Conference on Universal Algebra, Quasigroups and Related Systems held in Jadwisin, May 2328, 1989. Edited by A. Romanowska and J. D. H. Smith. Research and Exposition in Mathematics, 19. Heldermann Verlag, Berlin, 1992. viii+239 pp.

12. [FOM] Identities I suggest that your friend look @ the universal algebra literature. variety (also caIled an Equational class, due to Birkhoff s Theorem) of all algebras http://cs.nyu.edu/pipermail/fom/2007-January/011287.html

[FOM] identities Insall, Matt insall at umr.edu Sat Jan 20 14:41:40 EST 2007 Previous message: [FOM] identities Next message: [FOM] Identities Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... insall at umr.edu -Original Message- An "identity" is a sentence that can be expressed as the universal quaqntification of an ideintity. A friend has asked whether there is an algorithm for determining whether a given identity is implied by a given finite set of identities. Surely this is known to be unsolvable. References? Martin Previous message: [FOM] identities Next message: [FOM] Identities Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

13. CMS Winter 2003 Meeting universal algebra and Lattice Theory / Algèbre universelle et théorie des . that considers solvable congruences and algebras in a DPC Equational class. http://www.math.ca/Events/winter03/abs/ua.html

Org: Jennifer Hyndman (UNBC) ERIN BEVERIDGE, University of Northern British Columbia, Prince George, British Columbia Irresponsible homomorphisms and rank infinity Ross Willard has shown that rank can be used as a tool for determining if an algebra is strongly dualizable. In particular, if a dualizable algebra has finite rank then we know that the algebra is strongly dualizable. Determining if an algebra has rank infinity has previously been an ad-hoc process. We describe a process for showing that an algebra has rank infinity by introducing the concept of lifting dense sets and irresponsible homomorphisms. We demonstrate this process on an example family of algebras, ultimately showing that each algebra in the family is dualizable but not strongly dualizable. DAVID CASPERSON, University of Northern British Columbia, Prince George, British Columbia V2N 4Z9 A LDOR and universal algebra Many computer algebra packages and languages, for instance, M ATHEMATICA , GAP, or M APLE The A LDOR programming language (freely available from www.aldor.org

14. Universal Algebra - Wiktionary (uncountable) A branch of mathematics dealing with Equational classes of algebras, where similar theorems from disparate branches of algebra are unified. http://en.wiktionary.org/wiki/universal_algebra

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wiktionary"; universal algebra From Wiktionary Jump to: navigation search edit English edit Noun universal algebra Wikipedia has an article on: Universal algebra Wikipedia uncountable A branch of mathematics dealing with equational classes of algebras , where similar theorems from disparate branches of algebra are unified countable An algebraic structure studied therein. Retrieved from " http://en.wiktionary.org/wiki/universal_algebra Views Article Discussion Edit History Personal tools Log in / create account Navigation Main Page Community portal Requested entries Recent changes ... Contact us Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 01:38, 20 January 2007. Content is available under GNU Free Documentation License About Wiktionary

15. SBU Professor Page Graduate Courses (M.Sc., Ph.D) Advanced algebra, universal algebra, algebra in a Grothendieck Topos Injectivity in QuasiEquational Classes, http://en.sbu.ac.ir/Desktopmodules/Sbu_ProfessorsPage/ShowProffessor.aspx?userid

16. Re: Universal Algebra Question Re universal algebra Question Burris and Sankappanavar define an Equational class to be a class A of algebras such that A is precisely the class http://sci.tech-archive.net/Archive/sci.math/2006-10/msg05896.html

Re: Universal Algebra Question From (Arturo Magidin) Date : Sat, 21 Oct 2006 18:13:56 +0000 (UTC) Arturo Magidin wrote: Hello :) Burris and Sankappanavar define an "equational class" to be a class A of algebras such that A is precisely the class of algebras of some type F satisfying a set Sigma of identities of type F. My question is, is there a special name for an equational class which set Sigma of identities of type F? Or in English, the algebras that can be axiomatized by finitely many identities? Thank you very much =) Such equational classes are said to be "finitely based". Thank you very much Arturo Magidin =) As always, you are the unchallenged master of UA :) I wouldn't go that far, though I do seem to know a bit more about it than the average sci.math reader. One more question. If we have a variety, by Birkhoff, it is an equational class. If it happily turns out to be a finitely based equational class, is it proper to refer to it as a "finitely based variety" Yes; that is the usual terminology.

17. Birkhoff's Theorem -- From Wolfram MathWorld is called an Equational class if it is the class of algebras satisfying all Burris, S. and Sankappanavar, H. P. A Course in universal algebra. http://mathworld.wolfram.com/BirkhoffsTheorem.html

Search Site Algebra Applied Mathematics Calculus and Analysis ... Sakharov Birkhoff's Theorem Let and be two algebras over the same signature , with carriers and , respectively (cf. universal algebra is a subalgebra of if and every function of is the restriction of the respective function of on The (direct) product of algebras and is an algebra whose carrier is the Cartesian product of and and such that for every and all and all A nonempty class of algebras over the same signature is called a variety if it is closed under subalgebras, homomorphic images, and direct products. A class of algebras is said to satisfy the identity if this identity holds in every algebra from this class. Let be a set of identities over signature . A class of algebras over is called an equational class if it is the class of algebras satisfying all identities from . In this case, is said to be axiomatized by Birkhoff's theorem states that is an equational class iff it is a variety SEE ALSO: Birkhoff's Ergodic Theorem Universal Algebra Variety [Pages Linking Here] This entry contributed by Alex Sakharov author's link REFERENCES: Burris, S. and Sankappanavar, H. P.

18. 08: General Algebraic Systems Equational logic , by Walter Taylor, in Houston J. Math. 1979. This is a survey and a literature review of universal algebra. http://www.math.niu.edu/~rusin/known-math/index/08-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 08: General algebraic systems Introduction Here is an excerpt from the Math Reviews review of the book by Burris and Sankappanavar: For more information about this field, see that review (83k:08001) or 94d:08001. History Applications and related fields "Algebra" is a very broad section of mathematics; there are separate index pages here for specific algebraic categories (groups, fields, etc.) This heading focuses both on the broad principles covering all of algebra and on specific algebraic constructs not included in those other areas. By extension (and somewhat inappropriately) we use it to house a few resources discussing many areas of algebra. Universal algebra is arguably more a topic in Logic (03C05) (Model Theory), hence there is significant overlap. For Boolean algebras and generalizations see Ordered algebraic structures (06E) For groupoids, semigroups, and other multiplicative sets see Group Theory (sections 20L, 20M, 20N).

19. Universal Algebra Question Science Forum Index » Mathematics Forum » universal algebra Question. Page 1 of 1 Burris and Sankappanavar define an Equational class to be a class A http://www.groupsrv.com/science/about181326.html

Main Page Report this Page Enter your search terms Submit search form Web GroupSrv.com Loading.. Science Forum Index Mathematics Forum Page of Author Message Snis Pilbor Posted: Fri Oct 20, 2006 3:56 pm Guest Hello :) Burris and Sankappanavar define an "equational class" to be a class A of algebras such that A is precisely the class of algebras of some type F satisfying a set Sigma of identities of type F. My question is, is there a special name for an equational class which set Sigma of identities of type F? Or in English, the algebras that can be axiomatized by finitely many identities? Thank you very much =) Back to top Arturo Magidin Posted: Fri Oct 20, 2006 3:56 pm Guest Quote: Hello :) Burris and Sankappanavar define an "equational class" to be a class A of algebras such that A is precisely the class of algebras of some type F satisfying a set Sigma of identities of type F. My question is, is there a special name for an equational class which set Sigma of identities of type F? Or in English, the algebras that can be axiomatized by finitely many identities?

20. Re: Universal Algebra Question My question is, is there a special name for an Equational class which is precisely Previous by Thread, Re universal algebra Question, Snis Pilbor http://www.archivum.info/sci.math/2006-10/msg03630.html

sci.math Top All Lists Date Enter your search terms Submit search form Web www.archivum.info Thread Re: Universal Algebra Question from [ Arturo Magidin Subject Re: Universal Algebra Question From (Arturo Magidin) Date Sat, 21 Oct 2006 18:13:56 +0000 (UTC) Newsgroups sci.math Arturo Magidin wrote: > >Burris and Sankappanavar define an "equational class" to be a class A > Such equational classes are said to be "finitely based". Thank you very much Arturo Magidin =) As always, you are the unchallenged master of UA :) One more question. If we have a variety, by Birkhoff, it is an equational class. If it happily turns out to be a finitely based equational class, is it proper to refer to it as a "finitely based variety" More with this subject... Current Thread Universal Algebra Question Snis Pilbor Re: Universal Algebra Question Arturo Magidin Re: Universal Algebra Question Snis Pilbor Re: Universal Algebra Question Arturo Magidin Previous by Date: Re: Optimization problem... closed form solution? C6L1V@xxxxxxx Next by Date: Re: Prime ideals in the ring of continuous functions Arturo Magidin Previous by Thread: Re: Universal Algebra Question Snis Pilbor Next by Thread: The Toft Problem bill Indexes: Date Thread Top All Lists

21. IngentaConnect Equational And Implicational Classes Of Coalgebras Equational and implicational classes of coalgebras. Author Gumm H.P.1 to the theorems of Birkhoff and of Mal cev in classical universal algebra. http://www.ingentaconnect.com/content/els/03043975/2001/00000260/00000001/art001

var tcdacmd="dt"; Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); Equational and implicational classes of coalgebras Author: Gumm H.P. Source: Theoretical Computer Science , Volume 260, Number 1, 6 June 2001 , pp. 57-69(13) Publisher: Elsevier view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Keywords: Coalgebra Coequation Co-implication Covariety ... Mal'cev Language: English Document Type: Research article DOI: Affiliations: Fachbereich Mathematik und Informatik, Philipps Universitat Marburg, Hans Meerwein Strasse, D-35032 , Marburg, Germany

22. Brian Davey's Publications - Research Group On General Algebra And Its Applicati B. A. Davey, Topological duality for prevarieties of universal algebras, . B. A. Davey, Dualities for Equational classes of Brouwerian algebras and http://www.latrobe.edu.au/mathstats/maths/department/algebra-research-group/dave

Global Utilities La Trobe Home Skip to Content Contact La Trobe Sitemap Search: Global Navigation About La Trobe Campuses Faculties Research ... International Science, Technology and Engineering Faculty Home School Home Mathematics Home Current Students Prospective Students Postgraduate Students Organisational Unit La Trobe University Victoria 3086 AUSTRALIA Tel: Fax: Email: maths @latrobe.edu.au Research Group on General Algebra and its Applications Brian Davey's Publications Books Book Chapters Journal Articles: Mathematics Other Articles Books J. Pitkethly and B. Davey, Dualisability: Unary Algebras and Beyond , Springer, 2005. website B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Second edition , Cambridge University Press, 2002. website D. M. Clark and B. A. Davey, Natural Dualities for the Working Algebraist , Cambridge University Press, 1998. website B. A. Davey and H. A. Priestley, Introduction to Lattices and Order , Cambridge University Press, 1990. Book Chapters B. A. Davey and H. A. Priestley, Distributive lattices and duality General Lattice Theory B. A. Davey and I. G. Rosenberg

23. Universal Algebra@Everything2.com Much of the work done in universal algebra involves the study of class operators, Equational classes (varieties) and clones of operations. http://www.everything2.com/index.pl?node=universal algebra

24. Jezek On the equivalence between primitive classes of universal algebras Z. math. J.Jezek and T.Kepka Equational theories of medial groupoids algebra http://www.karlin.mff.cuni.cz/~jezek/

Jaroslav Jezek Programs 1. Groupoid 2. Lattice 3. FreeLat Picture pages 1. Damage of the Karlin Mathematics library 2. Czech forests Publications 1. JPG collections - papers and books not in TeX On the equivalence between primitive classes of universal algebras Z. math. Logik u. Grundl. Math. 14 (1968), 309-320 Reduced dimension of primitive classes of universal algebras (1968) CMUC 9 (1968), 103-108 Primitive classes of algebras with unary and nullary operations Colloquium Math. 20 (1969), 159-179 Principal dual ideals in lattices of primitive classes CMUC 9 (1968), 533-545 On categories of structures and classes of algebras Dissertationes Math. 75, Warszawa 1970 An embedding of groupoids and monomorphisms into simple groupoids CMUC 11 (1970), 91-98 On atoms in lattices of primitive classes CMUC 11 (1970), 515-532 The existence of upper semicomplements in lattices of primitive classes CMUC 12 (1971), 519-532 Upper semicomplements and a definable element in the lattice of groupoid varieties CMUC 12 (1971), 565-586 J.Jezek and L.Beran: On embedding of lattices in simple lattices

25. Alasdair Urquhart's Curriculum Vita ``Equational classes of distributive double palgebras , algebra universalis, . American Mathematical Society session on universal algebra, Boulder, http://www.science.uva.nl/~seop/archives/fall2000/subject-editors/urquhart.html

CURRICULUM VITAE ALASDAIR IAN FENTON URQUHART Professor of Philosophy University of Toronto Date of latest revision: April 1998 A. Biographical Information Personal Date of Birth: 20 December, 1945 Citizenship: British (Landed Immigrant 1970) Home address: 54 Boustead Avenue, Toronto, Ontario, M6R 1Y9 Home phone: 767-5240 (unlisted) University address: Department of Philosophy, University of Toronto, 215 Huron Street, Toronto, Ontario M5S 1A1 Office phone: 978-6789 Degrees M.A. Hons., University of Edinburgh, 1967 M.A. University of Pittsburgh, 1969 Ph.D. University of Pittsburgh, 1973 Title of Ph.D.Thesis: "The Semantics of Entailment" Supervisors: Profs. Nuel D. Belnap Jr. and Alan Ross Anderson Employment Present Appointment Professor, University of Toronto, 1986 - Associate Professor, University of Toronto, Erindale College, 1975-86 Date of appointment to Graduate School, 1973 Date of tenure award, Spring, 1975 Assistant Professor, University of Toronto, Erindale College, 1973-75 Lecturer, University of Toronto, Erindale College, 1970-73

26. Basic-Notions-abstract Abstract This paper reviews the basic properties of the Equational and This approach, based on universal algebra, facilitates the development of the http://www.labri.fr/perso/courcell/BasicNotions.html

BASIC NOTIONS OF UNIVERSAL ALGEBRA FOR LANGUAGE THEORY AND GRAPH GRAMMARS Bruno COURCELLE Abstract: Summary: Introduction 1 Basic notation 2 Many-sorted magmas 3 Polynomial systems and equational sets 4 Recognizable sets 5 Relationships between equational and recognizable sets 6 Inductively computable functions and Parikh's Theorem 7 Guide to the literature References Introduction The context-free and the regular languages are the two main classes of formal languages. We review how their basic concepts can be used for the description of sets of finite objects like trees, graphs, hypergraphs, tuples of words, traces (equivalence classes of words with respect to partial commutation). We shall review the general properties of recognizable sets and their relationships with equational ones. The result stating that the intersection of an equational set and a recognizable one is equational is fundamental and especially useful in constructions concerning context-free graph grammars. We shall also give a general form of Parikh's Theorem, with applications to equational sets of graphs, i.e., to context-free sets of graphs. Additional references and a correction: The finite automata recognizing sets of rooted, unordered, unranked trees were independently defined in:

27. Evelyn M. Nelson, Department Of Mathematics & Statistics @ McMaster University The next ten are primarily devoted to various aspects of Equational (or atomic) All this is, albeit within the general region of universal algebra, http://www.math.mcmaster.ca/talks/nelson_bio.php

Faculty Postdoctoral Fellows Administration/Staff Graduate Students ... Help Evelyn M. Nelson People Research Graduate Studies Undergraduate Studies ... Contact/Find Us McMaster Quick Links Evelyn M. Nelson An Appreciation B. BANASCHEWSKI Yes, university. After finishing grade 13 at Westdale High School in Hamilton, Evelyn went to the University of Toronto for the Mathematics-Physics-Chemistry Programme, a tough combined Honours course which for many years was regarded (and not only at its home institution) as the best course of its kind in the country. She took to the new existence with enormous delight and enthusiasm, and throughout her days she was fond of recalling the uplifting experience of her entry into university life, which indeed was to become her life for good. After two years at the University of Toronto she decided to transfer to McMaster University. We had a small but very active department in those days and were convinced - the renown of Toronto's "MPC" notwithstanding - that our Honours Mathematics course had something unique and substantial to offer. Thus when I, as the department chairman of the day, discussed her interest in transferring to us with thís obviously very bright and talented young woman, it momentarily occurred to me that she might have been attracted to us by our reputation. No such luck, though - the attraction of McMaster turned out to be of a very different sort: not long after she arrived she got married to Mort Nelson who was an undergraduate at McMaster at the time.

28. Publications Of George F. McNulty George F. McNulty, George F. Fifteen possible previews in Equational logic. Lectures in universal algebra (Szeged, 1983), 307331, Colloq. Math. Soc. http://www.math.sc.edu/~mcnulty/pubs/index.html

Publications of George F. McNulty George F. McNulty, George R. Holmes, deRosset Myers, Sandra Stader, and Angela Forand, Response Stability on a psychological instrument: A lattice theoretical supplement to traditional statistical measures, In progress. George F. McNulty and Ross Willard, The Chautauqua Problem, Tarski's Finite Basis Problem, and residual bounds for 3-element algebras , In progress. Ralph McKenzie, George F. McNulty and Ross Willard, Computational Recognition of Properties of Finite Algebras , In progress. Ralph Freese, Ralph N. McKenzie, Geroge F. McNulty, and Walter F. Taylor, Algebras, Lattices, Varieties. Vol. 2. , In progress. George F. McNulty and Ju Wang, The class of subdirectly irreducible groups generated by a finite group is finitely axiomatizable, Submitted. Online pdf view George F. McNulty, Zoltan Szekely, and Ross Willard, Equational complexity of the finite algebra membership problem. To appear in International Journal of Algebra and Computation. Online pdf view George F. McNulty, Residual finiteness and finite equational bases: undecidable properties of finite algebras Lectures on some recent work of Ralph McKenzie and Ross Willard. Preprint.

29. Sachgebiete Der AMS-Klassifikation: 00-09 68Q60} 03B80 Other applications of logic 03B99 None of the above but in this section 03Cxx Model theory 03C05 Equational classes, universal algebra, http://www.math.fu-berlin.de/litrech/Class/ams-00-09.html

Sachgebiete der AMS-Klassifikation: 00-09 nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen 01-XX 03-XX 04-XX 05-XX 06-XX 08-XX nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen

30. Variety (universal Algebra) - Indopedia, The Indological Knowledgebase In universal algebra, a variety is a class of algebraic structures of the same (in the sense of Birkhoff) is the same thing as an Equational class, http://indopedia.org/Variety_(universal_algebra).html

Indopedia Main Page FORUM Help ... Log in The Indology CMS Categories Abstract algebra Universal algebra Math stubs ... Wikipedia Article Variety (universal algebra) ज्ञानकोश: - The Indological Knowledgebase In universal algebra , a variety is a class of algebraic structures of the same signature satisfying a set of equations. According to Birkhoff's theorem , a variety (in the sense of Birkhoff) is the same thing as an equational class , namely the kind of variety mentioned in the introduction. That is, suppose we fix a signature model theory for example, that satisfy equations in a given set E . Those equations are statements from the predicate calculus involving universal quantifiers and equality only: each is a mathematical identity enforced in each model, for example the commutative law , or the absorption law On the other hand, variety take subalgebras take homomorphic images take cartesian products It is simple to see that an equational class satisfies these conditions, so that the burden of Birkhoff's theorem is the converse: classes of algebras that satisfy those conditions must be equational. This mathematics article is a stub . You can help Wikipedia by expanding it Retrieved from " http://indopedia.org/Variety_%28universal_algebra%29.html

31. Mathematics Subject Classification Index V. Pambuccian; 03C05 Equational classes, universal algebra G. Cupona; 03D40 Word problems G. Cupona; 03G25 Other algebras related to logic http://web.math.hr/glasnik/classindex.html

Glasnik Matematicki, Subject Index Index of papers published in Glasnik Matematicki from 2000 (Volume 35) to 2006 (Volume 41). Papers are listed according to the 2000 Mathematics Subject Classification . Items with * correspond to the earlier versions of the Mathematics Subject Classification (1991 and 1980). 03 MATHEMATICAL LOGIC AND FOUNDATIONS 03B30 Foundations of classical theories V. Pambuccian 03C05 Equational classes, universal algebra G. Cupona 03D40 Word problems G. Cupona 03G25 Other algebras related to logic W. A. Dudek 03E72 Fuzzy set theory S. A. Solovyov 04 SET THEORY* 04A10 Ordinal and cardinal numbers; generalizations* A. Mani 04A72 Fuzzy sets, fuzzy relations* S. A. Solovyov 05 COMBINATORICS 05B05 Block designs D. Held D. Crnkovic M. Essert S. Rukavina ... D. Crnkovic 05B07 Triple systems S. Markovski 05B30 Other designs, configurations V. Krcadinac 05C20 Directed graphs (digraphs), tournaments V. Neumann-Lara 05C70 Factorization, matching, covering and packing D. Vukicevic 05E20 Group actions on designs, geometries and codes D. Held

32. NMSU: Department Of Mathematical Sciences Basics of universal algebra and category theory. Theorems of Birkhoff and Tarski relating Equational classes, free algebras and their construction through http://www.math.nmsu.edu/Math.html

Skip navigation. New Mexico State University Personnel Tenure Track-Faculty College Track-Faculty Emerit-Adjunct Faculty Staff ... Math Success Center Student Information Undergraduate Courses Undergraduate Information Activities for Mathematics Majors Admissions ... NMSU Home College of Arts and Sciences Department of Mathematical Sciences You are here: NMSU Academics Arts and Sciences Mathematics ... Mathematics Catalog Course List Mathematics Catalog Course List MATH 451. Introduction to Differential Geometry 3 cr. Applies calculus to curves and surfaces in three dimensional Euclidean space. Prerequisites: MATH 280 and MATH 391, or consent of instructor. MATH 452. Foundations of Geometry 3 cr. Topics in projective, axiomatic Euclidean or non-Euclidean geometries. Prerequisite: either MATH 280, MATH 330, or MATH 331, or consent of instructor. MATH 453. Introduction to Topology 3 cr.

33. Fuzzy Equational Logic (Studies In Fuzziness And Soft Computing) | Free EBooks D Download Free eBookFuzzy Equational Logic (Studies in Fuzziness and Soft We therefore deal with topics traditionally studied in universal algebra. http://www.ebookee.com/Fuzzy-Equational-Logic-Studies-in-Fuzziness-and-Soft-Comp

Login Join User Search eBooks Technical Study Novel ... Game Fuzzy Equational Logic (Studies in Fuzziness and Soft Computing) Category: Technical Tag: Programming views since 2007-06-08. Description marketing Fuzzy Equational Logic (Studies in Fuzziness and Soft Computing) RapidShare FileFactory If you like it, BUY IT !!! MIRROR : DOWNLOAD FROM BRAVOSHARE* *All Countries Allowed Mirror: Download from Depositfiles.com MIRROR : IceFile.com Contents of this page are indexed from the original page for quick search purpose only. All actions are under your responsability. Email us to report illegal contents or external links and we'll remove them immediately. Search More... Fuzzy Equational Logic (Studies in Fuzziness and Soft Computing) Links No download links here Please check the description for download links if any or do a search to find alternative books. Can't Download? Please search mirrors if you can't find download links for "Fuzzy Equational Logic (Studies in Fuzziness and Soft Computing)" in " Description " and someone else may update the links. Check the comments when back to find any updates.

34. MATHEMATICAL STRUCTURES HANDBOOK OF LOGIC IN COMPUTER SCIENCE(Vol universal algebra in mathematics and computer science; Overview of the chapter Classes of algebras. Free, initial and final algebras; Equational logic http://www.mmsysgrp.com/hlcs1.htm

MATHEMATICAL STRUCTURES HANDBOOK OF LOGIC IN COMPUTER SCIENCE(Vol.1) by ABRAMSKY, GABBAY and MAIBAUM VALUATION SYSTEMS AND CONSEQUENCES Introduction Logics and Computer Science Summary Valuation Systems Satisfaction Valuation systems Modal logic and possible worlds Predicate language Summary Consequence relations and entailment relations Consequence relations Entailment relations The systems C and S4 Levels of implication Consequence operator Summary Proof theory and presentations Hilbert presentations Natural deduction presentations Natural deduction in sequent style Intuitionistic logic Gentzen sequent calculus for I Gentzen sequent calculus for C and S4 Properties of presentations Some further topics Valuation systems for I Maps between logics Correspondence theory Consistency RECURSION THEORY Introduction Opening remarks A taster Contents of the chapter Languages and notions of computibility Computibility and non-computibility Inductive definitions Recursion theory UNIVERSAL ALGEBRA Introduction What is universal algebra? Universal algebra in mathematics and computer science Overview of the chapter Historical notes Acknowledgments Prerequisites Examples of algebras Some basic algebras Some simple constructions Syntax and semantics of programs Synchronous concurrent algorithms Algebras and modularisation of software Algebras and morphisms Signatures and algebras Subalgebras Congruence and quotient algebras Homomorphisms and isomorphisms Direct products Abstract data types Constructions Subdirect products, residual and local properties

35. Hidden Algebra The paper Specifying, Programming and Verifying with Equational Logic, .. This book provides a systematic exposition of universal algebra and its http://www.cse.ucsd.edu/users/goguen/projs/halg.html

Hidden Algebra Homepage Contents Brief Overview Latest Hidden Results Brief Hidden Bibliography Interactive Examples ... Other Links A Brief Overview of Hidden Algebra Hidden algebra aims to give a semantics for software engineering, and in particular for concurrent distributed object systems, supporting correctness proofs that are as simple and mechanized as possible. This emphasis on effective proofs rather than semantic modelling is supported by taking a calculational approach based on equations , rather than one based on, for example, higher order logic, type theory, denotational semantics, or any particular kind of model or set theory, because equational proofs achieve maximal simplicity and mechanization, while still allowing adequate expressiveness. It is also convenient that the models of a hidden algebraic specification are precisely its possible implementations. Hidden algebra effectively handles the most troubling features of large systems, including concurrency, distribution, nondeterminism, and local states, as well as the usual features of the object paradigm, including classes, subclasses (inheritance), attributes and methods, in addition to supporting logical variables (as in logic programming), abstract data types, generic modules and more generally, the very powerful module system of prameterized programming. Hidden algebra generalizes the process algebra and transition system approaches to include non-monadic operations, so that it can take advantage of equations involving methods and attributes parameterized by data; this extra power can also dramatically simplify proofs. Coinduction methods appear to be more effective for behavioral properties (including behavioral refinement) than any alternative of which we are aware, and moreover, they can be automated to a very significant degree.

36. Mathematics - MATH Malcev conditions, congruence distributive Equational classes. Prerequisite(s) MATH 330 and MATH 425. 510 universal algebra II 4 hours. http://www.uic.edu/ucat/courses/MATH.html

Mathematics - MATH The information below lists courses approved in this subject area effective Spring 2008 . Not all courses will necessarily be offered these terms. Please consult the Schedule of Classes for a listing of courses offered for a specific term. 500-level courses require graduate standing. Back to Course Index Elementary Mathematics 3 hours. Rational operations and arithmetic, fundamental operations of algebra, linear equations and polynomials, graphing. Satisfactory/Unsatisfactory grading only. Not open to students with credit in MATH 090, MATH 092 or a mathematics course at or above the 100 level. No graduation credit. Prerequisite(s) : Eligibility determined by performance on the department placement test. Beginning Algebra 2 hours. Linear equations and inequalities, functions, linear functions, slope, exponents, polynomials, quadratic equations, rational expressions, rational equations, and applications. Satisfactory/Unsatisfactory grading only. Not open to students with credit in Math 070, 090, or a mathematics course at or above the 100-level. No graduation credit. Prerequisite(s) : Appropriate score on the department placement test.

37. Logic Seminar Abstracts Binding algebras A step from universal algebra to type theory. One has the apparatus of Equational logic, and, more widely firstorder logic, http://www-logic.stanford.edu/Abstracts/Seminar/Autumn98.html

Logic Seminar Abstracts Gordon Plotkin (University of Edinburgh) Binding Algebras: A step from universal algebra to type theory. We consider a number of topics based around the idea of seeking a good notion of abstract syntax for programming and other formal languages. The usual notion of the `abstract syntax' of a language is that it is given by the terms of a multi-sorted first-order signature. This has many advantages. Terms can be represented naturally as data structures of trees and one can then do meta-programming (e.g. in LISP or ML). One has the apparatus of equational logic, and, more widely first-order logic, for specification and other purposes. One can define programming languages by rewriting techniques, or by structural operational semantics. One can account for compositional denotational semantics by means of initial algebras and homomorphisms. Finally, one has a good notion of syntax-directed translation between different languages (as given by different signatures). We argue, however, that this is far from enough to account for many phenomena in programming or logical languages. For example there is no account of operations (e.g. integration, or quantification) that bind variables. Again there is no account of structured types, where types are themselves given by expressions of some formal language. We introduce and explore a notion of `binding algebras' to overcome the first difficulty. If there is time we will also discuss how `dependent algebra' may serve to overcome the second one.

38. George Voutsadakis algebraic Logic; Categorical and universal algebra; Ordered Structures Abstract algebraic Logic categorical algebraization of Equational logic, http://voutsadakis.com/RESEARCH/papers.html

George Voutsadakis Assistant Professor (with Tenure) School of Mathematics and Computer Science Lake Superior State University (On leave Spring 2008-Spring 2009, Department of Computer Science, Iowa State University) Research Interests Algebraic Logic Categorical and Universal Algebra Ordered Structures Combinatorics Theoretical Computer Science Mathematical Genealogy Technical Reports On Some Operations on Classes of Algebras and Coalgebras from a Bialgebraic Viewpoint pdf or postscript Probablistic Threshold Agent Networks pdf or postscript On the Categorical Mobius Calculus pdf or postscript Universal Bialgebra: Unifying Universal Algebra and Coalgebra pdf or postscript Combinatorial Analysis of the State Space Structure of Finite Automata Networks pdf or postscript Preprints Algebraic Logic Categorical Abstract Algebraic Logic: Tarski Congruence Systems, Logical Morphisms and Logical Quotients pdf or postscript Categorical Abstract Algebraic Logic: Generalized Tarski Congruence Systems pdf or postscript Categorical Abstract Algebraic Logic: Operations on Classes of Models pdf or postscript Categorical Abstract Algebraic Logic: Weakly Algebraizable pi-Institutions pdf or postscript Categorical Abstract Algebraic Logic: Closure Operators on Classes of PoFunctors pdf or postscript Categorical Abstract Algebraic Logic: Protoalgebraic Classes of Structure Systems pdf or postscript Categorical Abstract Algebraic Logic: Subdirect Representation for Classes of Structure Systems pdf or postscript Categorical Abstract Algebraic Logic: Selfextensional pi-Institutions with Implication

39. Hager, Madden: Majorizing-injectivity In Abelian Lattice-ordered Groups B3 B. Banaschewski, Injectivity and essential extensions in Equational classes of algebras, Proc. Conf. universal algebra, 1969; Queen s Papers in Pure http://www.numdam.org/numdam-bin/fitem?id=RSMUP_1983__69__181_0

40. Contents Of Term Rewriting And All That 3 universal algebra. 3.1 Terms, substitutions, and identities 3.2 algebras, homomorphisms 3.3 Free algebras 3.4 Term algebras 3.5 Equational classes http://www4.informatik.tu-muenchen.de/~nipkow/TRaAT/toc.html

Term Rewriting and All That Table of Contents Preface 1 Motivating Examples 2 Abstract Reduction Systems 2.1 Equivalence and reduction 2.1.1 Basic definitions 2.1.2 Basic results 2.2 Well-founded induction 2.3 Proving termination 2.4 Lexicographic orders 2.5 Multiset orders 2.6 Orders in ML 2.6.1 Lexicographic orders 2.6.2 Multiset orders 2.7 Proving confluence 2.7.1 Commutation 2.8 Bibliographic notes 3 Universal Algebra 3.1 Terms, substitutions, and identities 3.2 Algebras, homomorphisms, and congruences 3.3 Free algebras 3.4 Term algebras 3.5 Equational classes 4 Equational Problems 4.1 Deciding = E 4.2 Term rewriting systems 4.3 Congruence closure 4.4 Congruence closure on graphs 4.5 Syntactic unification 4.6 Unification by transformation 4.7 Unification and term rewriting in ML 4.8 Unification of term graphs 4.8.1 A quadratic algorithm 4.8.2 An almost linear algorithm 4.8.3 The complexity of sharing 4.9 Bibliographic notes 5 Termination 5.1 The decision problem 5.1.1 Undecidability in the general case 5.1.2 A decidable subcase

41. Aktuality The concept of a variety of algebras. Free algebras and the universal mapping property. Terms, identities, Equational classes. http://prf.upol.cz/english/PhD_04_05/P1101-AG.htm

Faculty of Science P1101 MATHEMATICS - ALGEBRA AND GEOMETRY The Department of Algebra nad Geometry offers training in five up-to-date fields of algebra : universal algebra (Prof. I. Chajda), ordered algebraic structures (Prof. J. Rachùnek), lattices and ordered sets (Dr. R. Halaš), fuzzy logic (Dr. R. Bìlohlávek), algebraic methods of data analysis (Dr. R. Bìlohlávek). These areas were self-contained branches of algebra in the last decades. Since then they have rapidly developed both on their own, as well as being tools for other mathematical disciplines. These areas of algebra are mainly applied in the mathematical foundations of computer science (theory of automata, formal languages, coding, etc.) and in the mathematical logic. Study plans contains courses in general algebra, lattice theory, varieties of algebra, ordered and lattice ordered groups and algebras, mathematical logic, model theory, and general topology. The main topic of our interest in universal algebra is the investigation of classes of algebras, especially varieties, their congruences and structure. Special kinds of identities and special algebra closure systems are also within our focus of interest. In ordered structures, the program is oriented toward special generalizations, e.g. semi-ordered groups and grupoids, special techniques and constructions of ordered and semi-ordered groups, MV-algebras and their generalizations, residuated groupoids, etc.

42. Algebra Class An algebraic equation represents a scale, what is done on one side of the . universal algebra studies common properties of all algebraic structures, . http://www.gradebook.org/Algrebra Class.htm

Home Sponsorship School Store Send an E-Card Net Primary Internet Lessons Primary School Main Student's Corner Teacher's Lounge Parent's Corner Departments English Electives ESL Foreign Languages ... Special Ed ucation Teacher's Lounge Parent's Corner Resources Colleges Distance Learning Expert Sites Education Sites ... Search this site or the web powered by FreeFind Site search Web search The Classroom does not claim all descriptions of sites to be their own words. "Love and you shall be loved. All love is mathematically just, as much as the two sides of an algebraic equation" Ralph Waldo Emerson Calculators Algebra Class Definition: " A branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. Algebra can include real numbers, complex numbers, matrices, vectors etc. Moving from Arithmetic to Algebra will look something like this: Arithmetic: 3 + 4 = 3 + 4 in Algebra it would look like: x + y = y + x Also Known As: Historically: al-jabr"

43. H. Peter Gumm - Publikationen H. Peter Gumm Equational and Implicational Classes of Coalgebras. H. Peter Gumm Geometrical reasoning and analogy in universal Algebras. http://www.mathematik.uni-marburg.de/~gumm/Papers/publ.html

Publications Books and Monograph H. Peter Gumm, Manfred Sommer 7. edition, Oldenbourg Verlag , (2006), 871 pages. (1. and 2. edition : Addison Wesley, 3., 4., 5.,6. and 7. edition: Oldenbourg Verlag). [Inhaltsverzeichnis] H. Peter Gumm : Geometrical Methods in Congruence Modular Varieties Memoirs of the American Mathematical Society , Number , (1983), 79 pages. [table of content] H. Peter Gumm, Werner Poguntke : Boolesche Algebra BI Taschenbuch, Band , Bibliographisches Institut Mannheim (1981), 95 pages. [full text, pdf 7.64 MB] H. Peter Gumm, ed., CMCS'03 - Coalgebraic Methods in Computer Science. Electronic Notes in Theoretical Computer Science, Vol. 82.1 (2003), 335 pp. [table of content] H. Peter Gumm : Universelle Coalgebra. Anhang (57 pp.) in dem Lehrbuch: Thomas Ihringer, Allgemeine Algebra. Berliner Studienreihe zur Mathematik, Band 10 (2003), Heldermann Verlag , 218 pp. [table of content] H. Peter Gumm (Guest editor) : Selected Papers of CMCS03. Theoretical Computer Science, vol. Elsevier B.V. . 221 pages. [table of content] Articles H. Peter Gumm :

44. Mathematical Structures: Equational Theory The Equational theory of a class of structures is the set of universal atomic formulas that hold in all members of the class. For a class of algebras, http://math.chapman.edu/cgi-bin/structures.pl?Equational_theory

45. Axiomatic Theory Of Formulas From Different Viewpoints - Universal Algebra, Cate So from the viewpoint of universal algebra, the theory of formulas is a case of any algebraic element, which is a solution of some algebraic equation, http://www.mathematics21.org/formulas-theory-views.html

google_ad_client = "pub-9523722979947731"; google_alternate_ad_url = "http://www.mathematics21.org/ads/728x15.html"; google_ad_width = 728; google_ad_height = 15; google_ad_format = "728x15_0ads_al"; google_ad_channel ="3391171102"; google_ad_client = "pub-9523722979947731"; google_ad_width = 728; google_ad_height = 90; google_ad_format = "728x90_as"; google_ad_channel ="3391171102"; google_alternate_ad_url = "http://www.mathematics21.org/ads/728x90"; google_ad_client = "pub-9523722979947731"; google_ad_width = 160; google_ad_height = 600; google_ad_format = "160x600_as"; google_ad_channel ="3391171102"; google_alternate_ad_url = "http://www.mathematics21.org/ads/160x600"; My homepage My math page My math news Donate for the research Axiomatic Theory of Formulas from Different Viewpoints This article is my own informal philosophical chatting around my formal math research. This online article by Victor Porton introduces Axiomatic Theory of Formulas (abbreviated ATF , which can be also instead deciphered Algebraic Theory of Formulas Mathematicians were Lazy Like in a humor story about a professor who searched for his glasses long time, and discovered them on his own nose... Mathematicians studied anything but not formulas; algebraic theory of formulas was discovered only in 2005 year. (The analogy is that formulas are like glasses through which mathematicians see, but the glasses themselves were unseen.)

46. Nelson Biography Defining a class of universal algebras to be algebraic if it is closed under In addition to The lattice of Equational classes of commutative semigroups http://www-history.mcs.st-andrews.ac.uk/~history/Biographies/Nelson.html

Evelyn Merle Roden Nelson Born: 25 Nov 1943 in Hamilton, Ontario, Canada Died: 1 Aug 1987 in Hamilton, Ontario, Canada Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index Version for printing Evelyn Nelson 's name before she married was Evelyn Merle Roden. Her parents were Russian immigrants who came to Canada in the 1920s and they were to have a strong influence in encouraging their daughter in her educational pursuits. Although her parents had struggled when they first arrived in Canada, by the time Evelyn was born they were comfortably off running a clothing business. Evelyn attended Westdale High School in Hamilton, Canada, and soon showed that she had quite outstanding gifts but it is very much to her parents credit that they encouraged her talents in science and mathematics although they themselves had little experience of these topics. Bernhard Banaschewski writes [ One of the most positive influences on her life ... was the unwavering reassurance she received from her parents. It was, indeed, not the easiest in those days for a girl to become passionately interested in mathematics and natural science, with many attitudes pervading the schools, and society at large, that were acting as powerful influences against such a choice. Thus it is very much to her parents' credit that they did everything possible to encourage her to follow her natural inclinations and innate talents, no matter how unfamiliar this might have appeared. They took the greatest pride in her scholastic successes ...

47. Transactions Of The American Mathematical Society E. Nelson, The lattices of Equational classes of commutative semigroups, Canad. P. Perkins, Bases for Equational theories of semigroups, J. algebra 11 http://www.ams.org/tran/2004-356-09/S0002-9947-03-03351-8/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6850(e) ISSN 0002-9947(p) Previous issue Table of contents Next issue Articles in press ... Next Article Definability in the lattice of equational theories of commutative semigroups Author(s): Andrzej Kisielewicz Journal: Trans. Amer. Math. Soc. MSC (2000): Primary 03C07; Secondary 03C05, 08B15, 20M07 Posted: October 28, 2003 Retrieve article in: PDF DVI PostScript Abstract ... Additional information Abstract: In this paper we study first-order definability in the lattice of equational theories of commutative semigroups. In a series of papers, J. Jezek, solving problems posed by A. Tarski and R. McKenzie, has proved, in particular, that each equational theory is first-order definable in the lattice of equational theories of a given type, up to automorphism, and that such lattices have no automorphisms besides the obvious syntactically defined ones (with exceptions for special unary types). He has proved also that the most important classes of theories of a given type are so definable. In a later paper, Jezek and McKenzie have ``almost proved" the same facts for the lattice of equational theories of semigroups. There were good reasons to believe that the same can be proved for the lattice of equational theories of commutative semigroups. In this paper, however, we show that the case of commutative semigroups is different. References:

48. METU MATHEMATICS DEPARTMENT MATH 344 Introduction to universal algebra (30)3 Lattices distributive and Groups acting on sets, Class equation. Statements of Sylow theorems and the http://www.math.metu.edu.tr/courses/undergrad.shtml

UNDERGRADUATE CURRICULUM FIRST YEAR First Semester MATH 111 Fundamentals of Math. (3-0)3 MATH 115 Analytic Geometry (3-0)3 MATH 153 Calculus for MATH. Students I (4-2)5 PHYS 111 Physics I (4-2)5 ENG 101 Development of Reading and Writing Skills I (4-0)4 Second Semester MATH 112 Introductory Discrete Math. (3-0)3 MATH 116 Basic Algebraic Structures (3-0)3 MATH 154 Calculus for MATH. Students II (4-2)5 PHYS 112 Physics II (Electricity and Magnetism) (4-2)5 ENG 102 Development of Reading and Writing Skills II (4-0)4 IS 100 Introduction to Information Systems and Applications NC SECOND YEAR Third Semester MATH 251 Advanced Calculus I (4-0)4 MATH 261 Linear Algebra I (4-0)4 CENG 230 Introduction to C Programming (2-2)3 ENG 211 Advanced Reading and Oral Communication (3-0)3 Fourth Semester MATH 252 Advanced Calculus II (3-2)4 MATH 254 Introduction to Differential Equations I (4-0)4 MATH 262 Linear Algebra II (4-0)4 HIST 2202 Principles of Kemal Atat?rk II NC A non-departmental elective (3-0)3 THIRD YEAR Fifth Semester MATH 349 Int. to Math. Analysis (4-0)4

49. Springer Online Reference Works The variety of universal algebras generated by a class consists of all quotient algebras may be replaced by the ary operation defined by the equation . http://eom.springer.de/v/v096320.htm

Encyclopaedia of Mathematics V Article referred from Article refers to Variety of universal algebras A class of universal algebras (cf. Universal algebra ) defined by a system of identities (cf. Algebraic systems, variety of ). A variety of universal algebras may be characterized as a non-empty class of algebras closed under taking quotient algebras, subalgebras and direct products. The last two conditions may be replaced by the requirement of closure under subdirect products. A variety of universal algebras is said to be trivial if it consists of one-element algebras. Every non-trivial variety of universal algebras contains a free algebra with basis of any cardinality. If and are bases of the same free algebra in a non-trivial variety and is infinite, then and are equipotent. The requirement that one of the bases be infinite is essential, but it may be omitted if the variety contains a finite algebra with more than one element. The variety of universal algebras generated by a class consists of all quotient algebras of subdirect products of algebras in . If a variety of universal algebras is generated by finite algebras, then every finitely-generated algebra in the variety is finite. The congruences of any algebra in a variety of universal algebras

50. Pure The later parts of each chapter gave deeper developments of the fields mentioned above and there were also included chapters on Equational classes http://www.library.tuiasi.ro/ipm/vol15no14/pure.html

PURE and APPLIED MATHEMATICS GENERAL LATTICE THEORY 2003, XIX + 663 pp., ISBN: 3-7643-6996-5 Basel - Boston - Berlin. Chapter II is entirely dedicated to Distributive Lattices. Characterization and representation theorems are presented in the 1st section. A lattice L is distributive if the two operations (inf or meet) and (sup or join) satisfy one of the equations or . By Lemma 10, these two equations are equivalent to each other and both of them to the inequality Let us quote Theorem 19 (G. Birkhoff - 1933 and M.H. Stone - 1936) that states that a lattice is distributive if and only if it is isomorphic to a ring of sets. Chapter V - Varieties of Lattices, starts with a first section presenting characterizations of varieties. Let us quote Theorem 3: A class K of lattices is a variety K is closed under the formation of homomorphic images, sublattices, and direct products. Theorem 6 (R. Ville - 1972) states that for any set of finite posets P, Var(P) is a variety of lattices ; Var(K) is the smallest variety containing K. The problem of finding equational bases is approached in Section 3. Theorem 5 (R.N. McKenzie - 1970) shows that any finite lattice has a finite equational basis. Amalgamation properties are studied in Section 4. A New Bibliography of 530 titles follows, and also a quite rich Index on 23 pages that closes this exceptional book.

51. Evelyn M. Nelson Her Ph.D. thesis, completed only a few months after the birth of her first child, was on The lattice of Equational classes of commutative semigroups, http://www.agnesscott.edu/Lriddle/women/nelson.htm

Biographies of W omen Mathematicians Home Alphabetical Index Chronological Index Resources ... Search Evelyn M. Nelson November 25, 1943 - August 1, 1987 Evelyn Merle Roden was born in Hamilton, Ontario of Russian immigrants. Banashcewki writes that One of the most positive influences on her life at that time, as well as during all later years, was the unwavering reassurance she received from her parents. It was, indeed, not the easiest in those days for a girl to become passionately interested in mathematics and natural science, with many attitudes pervading the schools, and society at large, that were acting as powerful influences against such a choice. Thus it is very much to her parents' credit that they did everything possible to encourage her to follow her natural inclinations and innate talents, no matter how unfamiliar this might have appeared. Abstract ]. Nelson taught at McMaster as a research associate for eight years before being given a position in the department at the associate professor level. She was promoted to full professor in 1983. Nelson wrote over 40 papers during a period of about 20 years and also served as the editor of Algebra Universalis. In the late 1970's, she began an investigation of algebraic problems arising in theoretical computer science, publishing several papers in computer science journals. From 1982 to 1984 she chaired the Unit of Computer Science within the mathematics department at McMaster. Nelson died at the age of 44 after battling cancer for several years.