Universal Algebra And Coalgebra

Author : Klaus Denecke,Shelly L. Wismath
Publisher : World Scientific
Page : 291 pages
File Size : 52,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812837455

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Universal Algebra and Coalgebra by Klaus Denecke,Shelly L. Wismath Pdf

The purpose of this book is to study the structures needed to model objects in universal algebra, universal coalgebra and theoretical computer science. Universal algebra is used to describe different kinds of algebraic structures, while coalgebras are used to model state-based machines in computer science.The connection between algebras and coalgebras provides a way to connect static data-oriented systems with dynamical behavior-oriented systems. Algebras are used to describe data types and coalgebras describe abstract systems or machines.The book presents a clear overview of the area, from which further study may proceed.

Author : Wolfgang Wechler
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642767715

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Universal Algebra for Computer Scientists by Wolfgang Wechler Pdf

A new model-theoretic approach to universal algebra is offered in this book. Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science. The notation is simple and the concepts are clearly presented. The book concerns the algebraic characterization of axiomatic classes of algebras (equational, implicational, and universal Horn classes) by closure operators generalizing the famous Birkhoff Variety Theorem, and the algebraic characterization of the related theories. The book also presents a thorough study of term rewriting systems. Besides basic notions, the Knuth-Bendix completion procedure and termination proof methods are considered. A third main topic is that of fixpoint techniques and complete ordered algebras. Algebraic specifications of abstract data types and algebraic semantics of recursive program schemes are treated as applications. The book is self-contained and suitable both as a textbook for graduate courses and as a reference for researchers.

Author : Clifford Bergman
Publisher : CRC Press
Page : 324 pages
File Size : 41,6 Mb
Release : 2011-09-20
Category : Computers
ISBN : 9781439851296

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Universal Algebra by Clifford Bergman Pdf

Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author’s two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff’s theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson’s lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ’s theorem on primal algebras and presents McKenzie’s characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.

Author : George M. Bergman
Publisher : Springer
Page : 572 pages
File Size : 54,5 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9783319114781

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An Invitation to General Algebra and Universal Constructions by George M. Bergman Pdf

Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

Author : Bart Jacobs
Publisher : Unknown
Page : 477 pages
File Size : 49,9 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 1316838560

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Introduction to Coalgebra by Bart Jacobs Pdf

Author : Bart Jacobs
Publisher : Cambridge University Press
Page : 495 pages
File Size : 43,5 Mb
Release : 2017
Category : Mathematics
ISBN : 9781107177895

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Introduction to Coalgebra by Bart Jacobs Pdf

An accessible introduction to coalgebra, with clear mathematical explanations and numerous examples and exercises.

Author : George A. Gratzer
Publisher : Princeton, N.J. : Van Nostrand
Page : 394 pages
File Size : 49,5 Mb
Release : 1968
Category : Algebra, Abstract
ISBN : UCAL:B4407349

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Universal Algebra by George A. Gratzer Pdf

Author : B. Csákány,Ervin Fried,Eligius Tamás Schmidt
Publisher : North Holland
Page : 814 pages
File Size : 43,8 Mb
Release : 1982
Category : Algebra, Universal
ISBN : UCAL:B4407354

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Universal Algebra by B. Csákány,Ervin Fried,Eligius Tamás Schmidt Pdf

Author : Ivan Chajda,G. Eigenthaler,Helmut Länger
Publisher : Unknown
Page : 252 pages
File Size : 55,7 Mb
Release : 2003
Category : Algebra, Universal
ISBN : UOM:39015058282206

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Congruence Classes in Universal Algebra by Ivan Chajda,G. Eigenthaler,Helmut Länger Pdf

Author : Roland Backhouse,Roy Crole,Jeremy Gibbons
Publisher : Springer
Page : 390 pages
File Size : 45,5 Mb
Release : 2003-07-31
Category : Computers
ISBN : 9783540477976

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Algebraic and Coalgebraic Methods in the Mathematics of Program Construction by Roland Backhouse,Roy Crole,Jeremy Gibbons Pdf

Program construction is about turning specifications of computer software into implementations. Recent research aimed at improving the process of program construction exploits insights from abstract algebraic tools such as lattice theory, fixpoint calculus, universal algebra, category theory, and allegory theory. This textbook-like tutorial presents, besides an introduction, eight coherently written chapters by leading authorities on ordered sets and complete lattices, algebras and coalgebras, Galois connections and fixed point calculus, calculating functional programs, algebra of program termination, exercises in coalgebraic specification, algebraic methods for optimization problems, and temporal algebra.

Author : Paul Moritz Cohn
Publisher : Unknown
Page : 360 pages
File Size : 52,5 Mb
Release : 1965
Category : Algebra, Universal
ISBN : STANFORD:36105031202554

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Universal Algebra by Paul Moritz Cohn Pdf

Author : Alexander Kurz,Marina Lenisa
Publisher : Springer
Page : 457 pages
File Size : 50,6 Mb
Release : 2009-09-19
Category : Computers
ISBN : 9783642037412

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Algebra and Coalgebra in Computer Science by Alexander Kurz,Marina Lenisa Pdf

This book constitutes the proceedings of the Third International Conference on Algebra and Coalgebra in Computer Science, CALCO 2009, formed in 2005 by joining CMCS and WADT. This year the conference was held in Udine, Italy, September 7-10, 2009. The 23 full papers were carefully reviewed and selected from 42 submissions. They are presented together with four invited talks and workshop papers from the CALCO-tools Workshop. The conference was divided into the following sessions: algebraic effects and recursive equations, theory of coalgebra, coinduction, bisimulation, stone duality, game theory, graph transformation, and software development techniques.

Author : Clifford Bergman
Publisher : Unknown
Page : 320 pages
File Size : 41,9 Mb
Release : 2011
Category : Electronic
ISBN : OCLC:1107412497

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Universal Algebra by Clifford Bergman Pdf

Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author's two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff's theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson's lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ's theorem on primal algebras and presents McKenzie's characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.

Author : Steven Shnider,Shlomo Sternberg
Publisher : International Press of Boston
Page : 528 pages
File Size : 44,8 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:39015032195029

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Quantum Groups by Steven Shnider,Shlomo Sternberg Pdf

An introduction to the field of quantum groups, including topology and statistical mechanics, based on lectures given at the Sackler Institute for Advanced Studies at Tel-Aviv University. Detailed proofs of the main results are presented and the bibliography contains more than 1260 references.

Author : David W. Jonah
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 40,6 Mb
Release : 1968
Category : Algebra, Universal
ISBN : 9780821812822

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Cohomology of Coalgebras by David W. Jonah Pdf