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1. FINITE SEMIGROUPS AND UNIVERSAL ALGEBRA
3 FINITE SEMIGROUPS AND universal algebra by Jorge Almeida (Univ. Contents Finite universal algebra Elements of universal algebra; Order and Topology;
http://www.wspc.com/books/mathematics/2481.html

Extractions: Motivated by applications in theoretical computer science, the theory of finite semigroups has emerged in recent years as an autonomous area of mathematics. It fruitfully combines methods, ideas and constructions from algebra, combinatorics, logic and topology. In simple terms, the theory aims at a classification of finite semigroups in certain classes called "pseudovarieties". The classifying characteristics have both structural and syntactical aspects, the general connection between them being part of universal algebra. Besides providing a foundational study of the theory in the setting of arbitrary abstract finite algebras, this book stresses the syntactical approach to finite semigroups. This involves studying (relatively) free and profinite free semigroups and their presentations. The techniques used are illustrated in a systematic study of various operators on pseudovarieties of semigroups. Contents: Finite Universal Algebra: Elements of Universal Algebra Order and Topology Finite Algebras Decidability Finite Semigroups and Monoids: Preliminaries Permutativity Operators Relating Semigroups and Monoids Semigroups Whose Regular D-Classes are Subsemigroups The Join The Semidirect Product The Power Factorization of Implicit Operations Open Problems

2. Computer Dictionary Definition Of Universal Algebra
Computer Dictionary Definition of universal algebra. Displaying all Computer dictionary definition of universal algebra. Related Words universal algebra.
http://www.realdictionary.com/computer/Computer/Universal-algebra.asp

3. Universal Algebra - InformationBlast
universal algebra Information Blast. universal algebra. Now this definition of group is problematic from the point of view of universal algebra.
http://www.informationblast.com/Universal_algebra.html

Extractions: Universal algebra is the field of mathematics that studies the ideas common to all algebraic structures 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 axioms , which in universal algebra must take the form of equational laws. An example is the associative axiom for a binary operation, which is given by the equation

4. On The Group Of Automorphisms Of Universal Algebra And Many Sorted Algebra
On the Group of Automorphisms of universal algebra and Many Sorted Algebra. 3 Ewa Burakowska. Subalgebras of the universal algebra. Lattices of subalgebras.
http://mizar.uwb.edu.pl/JFM/Vol6/autalg_1.html

Extractions: Association of Mizar Users The terminology and notation used in this paper have been introduced in the following articles [ On the Group of Automorphisms of Universal Algebra Some Properties of Many Sorted Functions On the Group of Automorphisms of Many Sorted Algebra On the Relationship of Automorphisms of 1-sorted and Many Sorted Algebras 1] Grzegorz Bancerek. Journal of Formalized Mathematics 2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences Journal of Formalized Mathematics 3] Ewa Burakowska. Subalgebras of the universal algebra. Lattices of subalgebras

5. Homomorphisms Of Algebras. Quotient Universal Algebra
Homomorphisms of Algebras. Quotient universal algebra. The second is concerned with the construction of a quotient universal algebra.
http://mizar.uwb.edu.pl/JFM/Vol5/alg_1.html

Extractions: Association of Mizar Users The terminology and notation used in this paper have been introduced in the following articles [ Homomorphisms of Algebras Quotient Universal Algebra 1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences Journal of Formalized Mathematics 2] Ewa Burakowska. Subalgebras of the universal algebra. Lattices of subalgebras Journal of Formalized Mathematics 3] Czeslaw Bylinski. Functions and their basic properties Journal of Formalized Mathematics 4] Czeslaw Bylinski. Functions from a set to a set Journal of Formalized Mathematics 5] Czeslaw Bylinski. Partial functions Journal of Formalized Mathematics 6] Czeslaw Bylinski.

6. Universal Algebra
NebulaSearch Home NebulaSearch Encyclopedia Top universal algebra. Main universal algebra, NebulaSearch article for universal algebra. Currently
http://www.nebulasearch.com/encyclopedia/article/Universal_algebra.html

7. Logic And Language Links - Universal Algebra
You have selected the concept universal algebra This concept has currently no gloss. universal algebra is a subtopic of algebra 1 subtopic of model theory.
http://staff.science.uva.nl/~caterina/LoLaLi/Pages/11.html

8. Universal Algebra
http://staff.science.uva.nl/~yde/teaching/ua/

Extractions: Make the following exercises from the book: Third homework set (deadline: June 12, 2002). Prove from first principles (i.e. only use results proved in section 10) that if F is free for K over X, then F is also free for HSP(K) over X. Let M be the variety of monadic (or S5-)algebras; you may think of M as the class of subalgebras of complex algebras of frames (W,R) in which R is an equivalence relation.

9. Faculty Of Sciences - Vrije Universiteit Amsterdam
universal algebra and Logic. There has been a shift of interests towards relation algebra and logic in the last few years. This is
http://www.math.vu.nl/geom/universal-en.html

Extractions: Links There has been a shift of interests towards relation algebra and logic in the last few years. This is due in part to the supervising of - and participating in - M. El Bachraoui's Ph.D. research in the area of relation algebra. The running project is currently suspended, though there may be occasional future work in the field of convex geometry. The project universal algebra and logic is basically involved with Tarski's relation algebras, which provide an algebraic model of a Boolean algebra of binary relations with composition and reverse operators. The joint research of M. El Bachraoui and M. van de Vel has sofar been directed to questions on representability (when does an algebra models a Boolean algebra with genuine binary relations), degree (how many variables are required for the statements and proofs of results in a particular subtheory), and tensor products (a general construction capturing matrix relation algebras and other derived constructions). The language and logic of relation algebra was used by Tarski for a faithful embedding of set theory and of number theory. Recently, M. van de Vel extended this result to obtain a faithful translation of any first order theory into a theory of relation algebra with features (allowing record-like constructs in the language). The language of relation algebra with features seems particularly appropriate to express programming constructs like

10. Universal Algebra, Algebraic Logic, And Databases|KLUWER Academic Publishers
Books » universal algebra, Algebraic Logic, and Databases. universal algebra, Algebraic Logic, and Databases. Add to cart. by B. Plotkin
http://www.wkap.nl/prod/b/0-7923-2665-2

Extractions: This volume is devoted to the development of an algebraic model of databases. The first chapter presents a general introduction. The following sixteen chapters are divided into three main parts. Part I deals with various aspects of universal algebra. The chapters of Part I discuss topics such as sets, algebras and models, fundamental structures, categories, the category of sets, topoi, fuzzy sets, varieties of algebras, axiomatic classes, category algebra and algebraic theories. Part II deals with different approaches to the algebraization of predicate calculus. This material is intended to be applied chiefly to databases, although some discussion of pure algebraic applications is also given. Discussed here are topics such as Boolean algebras and propositional calculus, Halmos algebras and predicate calculus, connections with model theory, and the categorial approach to algebraic logic. Part III is concerned specifically with the algebraic model of databases, which considers the database as an algebraic structure. Topics dealt with in this part are the algebraic aspects of databases, their equivalence and restructuring, symmetries and the Galois theory of databases, and constructions in database theory. The volume closes with a discussion and conclusions, and an extensive bibliography.

Books » universal algebra. universal algebra. Add to cart. by PM Cohn Professor Emeritus, Bedford College, University of London, UK
http://www.wkap.nl/prod/b/90-277-1254-9

12. Index Of /~insall/Research/Universal Algebra
Parent Directory 22Jan-2003 1436 - Polynomial_CompletenIndex of /~insall/Research/universal algebra. Name Last modified Size
http://web.umr.edu/~insall/Research/Universal Algebra/

13. Elementary Universal Algebra And Computer Science
Elementary universal algebra and Computer Science. Eric G. Wagner, Wagner Mathematics universal algebra is a branch of mathematics
http://www.ii.uib.no/~fredrikm/seminar/wagner.html

Extractions: Universal algebra is a branch of mathematics which was originally concerned with abstract generalizations of algebraic concepts. It is perhaps surprising then that the ideas of universal algebra have played a significant role in such areas of computer science as the specification of data types, the semantics of programming languages, and the theory of compilers. Equally surprising is that the seemingly abstract fundamental constructs of universal algebra can be easily implemented on a computer using a symbolic computation system such as Mathematica in a manner that makes it possible to construct and explore interesting computer science examples. In this talk we will give an introduction to universal algebra for non-mathematicians, illustrate its application to the syntax and semantics of programming languages, and describe how the basic constructs of universal algebra can be implemented within Mathematica. Demonstrations of the Mathematica programs (notebooks) implementing the material in the talk will be given on a later date and, if there is sufficient interest, more detailed talks may also be given.

14. Universal Algebra For Computer Scientists
UNIVERAL ALGEBRA for Computer Scientists (click on the top line of the title to get started) A course in universal algebra (and related mathematics
http://www.ii.uib.no/~wagner/UASCR/cover01.htm

15. Universal Algebra From FOLDOC
universal algebra. logic The model theory of firstorder equational logic. (1997-02-25). Try this search on OneLook / Google. Nearby
http://www.nue.org/foldoc/foldoc.cgi?Universal algebra

16. The Assayer Course In Universal Algebra, A
Course in universal algebra, A. Authors,
http://www.theassayer.org/cgi-bin/asbook.cgi?book=330

17. Universal Algebra Definition Meaning Information Explanation
universal algebra definition, meaning and explanation and more about universal algebra. FreeDefinition - Online Glossary and Encyclopedia, universal algebra.
http://www.free-definition.com/Universal-algebra.html

Extractions: 3 Further issues 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

18. Algebraic Logic And Universal Algebra In Computer Science 1988
Algebraic Logic and universal algebra in Computer Science 1988 Ames, Iowa, USA. 181194; Ivo G. Rosenberg Mal cev algebras for universal algebra terms.
http://www.informatik.uni-trier.de/~ley/db/conf/aluacs/aluacs1988.html

Extractions: Clifford Bergman Roger D. Maddux Don Pigozzi (Eds.): Algebraic Logic and Universal Algebra in Computer Science, Conference, Ames, Iowa, USA, June 1-4, 1988, Proceedings. Lecture Notes in Computer Science 425 Springer 1990, ISBN 3-540-97288-9 DBLP Isidore Fleischer : The abstract Galois theory: a survey. 133-137 : The implications in conditional logic. 139-159 Lawrence S. Moss Satish R. Thatte : Optimal semantics of data type extensions. 161-180 G. C. Nelson : Other logics for (equational) theories. 181-194 Ivo G. Rosenberg : Mal'cev algebras for universal algebra terms. 195-208 : Beth's and Craig's properties via epimorphisms and amalgamation in algebraic logic. 209-225

19. Algebraic Logic And Universal Algebra In Computer Science
dblp.unitrier.de Algebraic Logic and universal algebra in Computer Science. Algebraic Logic and universal algebra in Computer Science 1988 Ames, Iowa, USA.
http://www.informatik.uni-trier.de/~ley/db/conf/aluacs/

20. Finite Semigroups And Universal Algebra
Author Jorge Almeida; Title Finite Semigroups and universal algebra; Publisher World Scientific, Singapore; Date 1995; ISBN 981
http://www.fc.up.pt/cmup/jalmeida/FSUA/FSUA.html

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