21. A Sketch Of The Prehistory Of Universal Algebra In the case of universal algebra what suggests itself as the beginning, Here the definition of a universal algebra appears for the first time and the http://www.maths.utas.edu.au/People/dfs/Papers/GrassmannUAlgpaper/node2.html

NEXT PAGE CONTENTS PREVIOUS PAGE A Sketch of the Prehistory of Universal Algebra There are some branches of mathematics to which one may arguably assign a clearly defined starting point. In the case of Universal Algebra what suggests itself as the beginning, at least in a narrow sense, is Garrett Birkhoff's paper [1] On the Structure of Abstract Algebras which appeared in the Proceedings of the Cambridge Philosophical Society in 1935. Here the definition of a Universal Algebra appears for the first time and the broad outlines of the subject may already be discerned. In particular ``abstract algebras are divided by a very simple scheme into self-contained `species'. Within each species a perfect duality is found between families of formal laws and the families of algebras satisfying them''. Here the term ``family of algebras of a given species'' is used in a technical sense meaning a class closed under taking subalgebras, homomorphic images and direct products - or what is nowadays called a variety This said, one must point out that undoubtedly the most influential figure in the movement towards abstraction and generality in algebra which culminated in Universal Algebra was Emmy Noether, who died in 1935. In the twenties her school had investigated the notion of a group with operators, which is already very general, including, for example, groups, rings and linear spaces. As Birkhoff himself said in 1946 [2] ``they had developed many of the most important ideas of Universal Algebra'' - for example, the three fundamental isomorphism theorems, which are now recognized as theorems of Universal Algebra, were given for groups with operators in van der Waerden's

22. Mgehrke.html New Mexico State University Nonstandard mathematics, operators on boolean algebras, fuzzy mathematics, universal algebra, general topology, posets and lattices. http://www.math.nmsu.edu/mgehrke/mgehrke.html

Mai Gehrke Department of Mathematical Sciences Phone: (505] 646-4218 New Mexico State University Fax: (505) 646-1064 Las Cruces NM mailto:%20mgehrke@nmsu.edu Office Location: Science Hall Room 232 Return to Faculty Page Return to Main Index PROFESSIONAL EXPERIENCE Visiting Professor, Technical University of Denmark Lyngby Denmark /044/05 Visiting Lektor University of Copenhagen Copenhagen Denmark Visitor, University of Oxford Oxford United Kingdom Professor, New Mexico State University Las Cruces New Mexico Part-time consulting, Physical Science Laboratory, Las Cruces New Mexico 1/975/97 Visiting Professor, Vanderbilt University Nashville Tennessee 8/9612/96 Visiting Lektor University of Copenhagen Copenhagen Denmark 8/93 5/00 Associate Professor, New Mexico State University Las Cruces New Mexico 8/905/93 Assistant Professor, New Mexico State University Las Cruces New Mexico 8/885/90 2-year position as Assistant Professor, Vanderbilt University Nashville Tennessee Assistante Associée Université de Nice, Nice France Assistante Associée Université de Haute Alsace Mulhouse France Teaching Assistant

23. Universal Algebra And Lattice Theory University of Szeged Conference on universal algebra AND LATTICE THEORY Szeged, July 48, 2005 email algconf@math.uszeged.hu http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

24. UA Colleagues in general algebra and related fields universal algebra discussion group (moderated by Bill Rowan). • A general algebra calculator program http://spot.colorado.edu/~kearnes/ua.html

General Algebra Lattice Theory Conferences in general algebra Colleagues in general algebra and related fields Mathematical Structures home page (maintained by Peter Jipsen) Universal algebra and lattice theory bibliographic database (maintained by Ralph Freese) Universal algebra discussion group (moderated by Bill Rowan) A general algebra calculator program (written by Ralph Freese and Emil W. Kiss) Related Links Algebra Universalis home page Homepage of the Arbeitstagung Allgemeine Algebra (AAA) Research group on general algebra and its applications at La Trobe University Dresden formal concept analysis page ... Mathematical Logic around the world

25. Keith A. Kearnes University of Colorado. Algebra, Logic, Combinatorics. Resources in general algebra, universal algebra and lattice theory. http://spot.colorado.edu/~kearnes/

Keith A. Kearnes Mathematics Contact Keith A. Kearnes Department of Mathematics Research ... University of Colorado Boulder CO 80309-0395 Teaching

26. Catalogue Of Algebraic Systems. For a brief introduction and some history see Hermann Grassmann and the Prehistory of universal algebra by Desmond FearnleySander http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

27. Conferences In General Algebra And Related Fields universal algebra and Lattice Theory, University of Szeged, Hungary, July 48, 2005. Intermediate Problems of Model Theory and universal algebra, http://spot.colorado.edu/~kearnes/conf.html

Conferences in General Algebra and Related Fields 2006 ASL Annual Meeting , Montreal, Canada, May 17-21, 2006. 2006 AMS-MAA Joint Meeting (with a special session on ``The Many Lives of Lattice Theory, the Theory of Ordered Sets, and Universal Algebra''), San Antonio, TX, January 12-15, 2006. Second Conference on Mathematical Methods in Counterterrorism and Computer Security, Benedict College and UWI Institute for Mathematical Methods in Counterterrorism, Columbia, SC, November 1-3, 2005. (Contact lattice@math.harvard.edu if interested.) 2005 Fall Central Section Meeting of the AMS (with a special session on Universal Algebra and Order), University of Nebraska, Lincoln, NE, October 21-23, 2005. Summer School on General Algebra and Ordered Sets, Mala Moravka, Czech Republic, September 4-10, 2005. (Contact the organizers at chajda@inf.upol.cz ... International Algebraic Conference , Ural State University, Ekaterinburg, Russia, August 29-September 3, 2005. 9th Asian Logic Conference , Novosibirsk, Russia, August 16-19, 2005. Logic in Hungary, 2005

28. ERLOGOL-2005 Model theory and universal algebra. Mathematics Institute at the State Technical University in Novosibirsk, Russia. June 26 to July 21, 2005. http://www.ams.org/mathcal/info/2005_jun26-jul1_novosibirsk.html

29. Mai Gehrke's Curriculum Vita New Mexico State University Nonstandard mathematics, operators on boolean algebras, fuzzy mathematics, universal algebra, general topology, posets http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

30. Universal Algebra And Lattice Theory Bibliography The University of Hawaii and Alan Day Memorial. universal algebra and Lattice Theory Bibliographic Database. Instructions.Start by entering the last name http://www.math.hawaii.edu/~ralph/Bib/

The University of Hawaii and Alan Day Memorial Universal Algebra and Lattice Theory Bibliographic Database Instructions. Start by entering the last name (capitalized correctly but accents omitted) of someone (perhaps yourself) in the Author field and leaving the other fields blank. Or enter one or two words in the Title field. After playing a little be sure to update your own entries. Detailed instructions Ways to use the database History of the database ... Making corrections and additions to the database Output Format: BibTeX AmSTeX Author: Title: Journal: Year: This page is changing frequently; you may need to press the reload button on your browser. Modifying the Database Add new entries to the database. Change an entry in the database. Last modified: 17 April 1996 Ralph Freese ralph@math.hawaii.edu

31. Prof. Kaiser University of Houston Mathematical logic, universal algebra, lattice theory and logic programming. http://math.uh.edu/~klaus/

Klaus Kaiser Professor of Mathematics, University of Houston Office: 607 PGH Office Phone: (713)-743-3462 Office Hours: TTH 12-1 The easiest way to reach me is by sending e-mail to kkaiser@uh.edu . Students and UH colleagues should use my other e-mail: klaus@math.uh.edu . You may also send me snail-mail via the Department of Mathematics, University of Houston, Houston, TX77204-3476. During the fall I will be teaching the graduate Math 6302, Modern Algebra First Info about the Fall 2005 Online Course Math 5397, Discrete Mathematics I came to the University of Houston in 1969 with a degree from the University of Bonn (PhD 1966, Habilitation 1973, Darmstadt). My main research interests are in Mathematical Logic, Universal Algebra, Lattice Theory and Logic Programming. Some of my papers, e.g., on quasi-universal and projective model classes are with Manfred Armbrust who retired from the University of Cologne. A paper on non-standard lattice theory is with two of my former Ph.D. students Mai Gehrke and Matt Insall . We had this paper dedicated to Abraham Robinson. Since June 1996, I am the Managing Editor of the

32. An Algebra Calculator Program. The universal algebra Calculator is a mathematical program. It performs computations related S. Burris, HP Sankappanawar A course in universal algebra. http://www.math.hawaii.edu/~ralph/software/uaprog/

An algebra calculator program The Universal Algebra Calculator is a mathematical program. It performs computations related to general algebraic structures. Authors: Ralph S. Freese (ralph at math hawaii edu) Emil W. Kiss (ewkiss at cs elte hu) New Easy Downloading and Running!! Mac OS X Windows Linux Solaris ... Directions to quickly see the program in action! Contents Main features and availability Recommended use Conditions of use Getting the program ... History and acknowledgments Main features and availability The present version has the following math functionalities: Form direct products. Create a factor algebra. Generate a subalgebra in a direct power. Create free algebras in a finitely generated variety. Compute the congruence lattice of an algebra. Compute the Tame Congruence Theoretic type labeling. Compute four types of centrality. Compute all unary polynomials. Compute minimal neighborhoods. The program has a Graphical User Interface to access these functionalities via menus. In addition, this interface provides the facilities to Create and edit algebras using operation tables.

33. Lattices, Universal Algebra And Applications This conference was organized by the Project Lattices, universal algebra and Algebraic Logic of the Centro de Álgebra da Universidade de Lisboa (CAUL). http://www.lmc.fc.ul.pt/~uaconf03/

Lattices, Universal Algebra and Applications Lisbon May 28-30, 2003 CAUL The conference included six invited lectures and about thirty contributed talks. Over 60 participants came from all over Europe, plus Japan, Canada and the United States. Larger picture Main Speakers Program and Abstracts Conference fee ... Organizing Committee Conference location The conference took place at the Complexo Interdisciplinar da Universidade de Lisboa , Avenida Professor Gama Pinto, 2, 1609-003 LISBOA. Maps and directions can be obtained from CAUL's website Invited speakers W. Blok (University of Illinois at Chicago) M. Gehrke (New Mexico State University) M. Haviar (Matej Bel University) K. Kearnes (University of Colorado) B. Monjardet (University of Paris I) D. Mundici (University of Florence) Organizing Committee Gabriela Bordalo (CAUL, University of Lisbon) Isabel Ferreirim (CAUL, University of Lisbon) Program and Abstracts The Conference Program is available, in

34. Lattices, Universal Algebra And Applications Lisbon, Portugal; 2830 May 2003. http://www.ptmat.fc.ul.pt/~uaconf03/

Lattices, Universal Algebra and Applications Lisbon May 28-30, 2003 CAUL The conference included six invited lectures and about thirty contributed talks. Over 60 participants came from all over Europe, plus Japan, Canada and the United States. Larger picture Main Speakers Program and Abstracts Conference fee ... Organizing Committee Conference location The conference took place at the Complexo Interdisciplinar da Universidade de Lisboa , Avenida Professor Gama Pinto, 2, 1609-003 LISBOA. Maps and directions can be obtained from CAUL's website Invited speakers W. Blok (University of Illinois at Chicago) M. Gehrke (New Mexico State University) M. Haviar (Matej Bel University) K. Kearnes (University of Colorado) B. Monjardet (University of Paris I) D. Mundici (University of Florence) Organizing Committee Gabriela Bordalo (CAUL, University of Lisbon) Isabel Ferreirim (CAUL, University of Lisbon) Program and Abstracts The Conference Program is available, in

35. Universal Algebra: Information From Answers.com universal algebra universal algebra is the field of mathematics that studies the ideas common to all algebraic structures. http://www.answers.com/topic/universal-algebra

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping universal algebra Wikipedia universal algebra Universal algebra is the field of mathematics that studies the ideas common to all algebraic structures Basic idea From the point of view of universal algebra, an algebra (or abstract algebra ) is a set A together with a collection of operations on A . An n ary operation on A is a function that takes n elements of A and returns a single element of A . Thus, a 0-ary operation (or nullary operation ) is simply an element of A , or a constant , often denoted by a letter like a . A 1-ary operation (or unary operation ) is simply a function from A to A , often denoted by a symbol placed in front of its argument, like ~ x . A 2-ary operation (or binary operation ) is often denoted by a symbol placed between its arguments, like x y . Operations of higher or unspecified arity are usually denoted by function symbols, with the arguments placed in parentheses and separated by commas, like f x y z ) or f x x n After the operations have been specified, the nature of the algebra can be further limited by

36. Math Subject Matter Algebra Univalg Mailing List Mailing list for use by the universal algebra community. universal algebra is a technical branch of mathematics related to algebra http://www.teach-nology.com/teachers/subject_matter/math/algebra/

Curriculum Lesson Plans Organizers Rubrics ... Abstract Algebra - Lecture notes by David Wilkins, Trinity College, Dublin. Topics in Number Theory; Group Theory; Galois Theory. Abstract and Linear Algebra - A forum for students on abstract algebra and linear algebra. Abstract Algebra Online - This site contains many of the definitions and theorems from the area of mathematics generally called abstract algebra. It is intended for undergraduate students taking an abstract algebra class at the junior/senior level, as well as for students taking their first graduate algebra course. It is based on the following books. Algebra Avenue - "Have you ever needed interactive online algebra help from a talking voice, or an online algebra tutor to improve your grades? Well this program is made for you! Talking interactive online algebra tutor homework help with online algebra practice problems & tutorials." Algebra Links - From Spartanburg County School District Two.

37. Universal Algebra - Definition Of Universal Algebra In Encyclopedia universal algebra is the field of mathematics that studies the ideas common to all algebraic structures.Contents showTocToggle( show , hide )1 Basic idea2 http://encyclopedia.laborlawtalk.com/Universal_algebra

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law Universal algebra is the field of mathematics that studies the ideas common to all algebraic structures Contents showTocToggle("show","hide") 1 Basic idea 2 Examples 2.1 Groups 2.2 Modules ... 5 External links Basic idea From the point of view of universal algebra, an algebra is a set A together with a collection of operations on A . An n ary operation on A is a function that takes n elements of A and returns a single element of A . Thus, a 0-ary operation (or nullary operation ) is simply an element of A , or a constant , often denoted by a letter like a . A 1-ary operation (or unary operation ) is simply a function from A to A , often denoted by a symbol placed in front of its argument, like ~ x . A 2-ary operation (or binary operation ) is often denoted by a symbol placed between its arguments, like x y . Operations of higher or unspecified arity are usually denoted by function symbols, with the arguments placed in parentheses and separated by commas, like f x y z ) or f x x n After the operations have been specified, the nature of the algebra can be further limited by

38. Kids.net.au - Encyclopedia Universal Algebra - universal algebra is the field of mathematics that studies the ideas common to all From the point of view of universal algebra, an algebra is a set A http://www.kids.net.au/encyclopedia-wiki/un/Universal_algebra

Web kids.net.au Thesaurus Dictionary Kids Categories Encyclopedia ... Contents Encyclopedia - Universal algebra Universal algebra is the field of mathematics that studies the ideas common to all algebraic systems[?] Table of contents showTocToggle("show","hide") 1 Basic idea 2 Examples 2.1 Groups 2.2 Modules ... 3 Further issues Basic idea From the point of view of universal algebra, an algebra is a set A together with a collection of operations on A . An n -ary operation on A is a function that takes n elements of A and returns a single element of A . Thus, a 0-ary operation (or nullary operation ) is simply an element of A , or a constant , often denoted by a letter like a . A 1-ary operation (or unary operation ) is simply a function from A to A , often denoted by a symbol placed in front of its argument, like ~ x . A 2-ary operation (or binary operation ) is often denoted by a symbol placed between its arguments, like x y . Operations of higher or unspecified arity are usually denoted by function symbols, with the arguments placed in parentheses and separated by commas, like f x y z ) or f x x n After the operations have been specified, the nature of the algebra can be further limited by

39. Universal Algebra In Combinatory Logic universal algebra in Combinatory Logic. This was the starting point of universal algebra, where the objects of interest the structures - were http://www.isbe.ch/~amrhein/diss/diss.html

Universal Algebra in Combinatory Logic Beatrice Amrhein Introduction The strong influence of computer science on mathematics is causing a growing interest in the concept of functions as algorithms. Considering functions as operations or rules in their full generality, they can be applied to any argument. For example, we may think of a function as a program that operates on other programs. In particular, self application is allowed. combinatory completeness : Any applicative expression built up from functions may not only be regarded as a function, but also represented by a combinator. Models of this theory are called combinatory algebras . They are of the form , where A is some set, a binary operation on A and where combinatory completeness is satisfied. They arise whenever a mathematical structure is furnished with a notion of internal computability. It was in the same decade that it became clear that (classical) algebra deals not primarily with the manipulation of sums and products of numbers, but with sums and products of elements of any sort - under the assumption that these operations satisfy the appropriate basic axioms . This was the starting point of universal algebra , where the objects of interest - the structures - were presented by use of axioms over operations and morphisms between them.

40. Universal Algebra -- Facts, Info, And Encyclopedia Article Categories universal algebra, Abstract algebra universal algebra is the field of (A science (or group of related sciences) dealing with the logic of http://www.absoluteastronomy.com/encyclopedia/u/un/universal_algebra.htm

Universal algebra [Categories: Universal algebra, Abstract algebra] Universal algebra is the field of (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics that studies the ideas common to all (Click link for more info and facts about algebraic structure) algebraic structure s. Basic idea From the point of view of universal algebra, an algebra (or abstract algebra ) is a set A together with a collection of operations on A . An n (Click link for more info and facts about ary) ary operation on A is a (A mathematical relation such that each element of one set is associated with at least one element of another set) function that takes n elements of A and returns a single element of A . Thus, a 0-ary operation (or nullary operation ) is simply an element of A , or a (A number representing a quantity assumed to have a fixed value in a specified mathematical context) constant , often denoted by a letter like a . A 1-ary operation (or (An operation with exactly one operand) unary operation ) is simply a function from A to A , often denoted by a symbol placed in front of its argument, like ~ x . A 2-ary operation (or (An operation that follows the rules of boolean algebra; each operand and the result take one of two values)

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