A Course In Universal Algebra

Author : S. Burris,H. P. Sankappanavar
Publisher : Springer
Page : 276 pages
File Size : 48,5 Mb
Release : 2011-10-21
Category : Mathematics
ISBN : 1461381320

Get Book

A Course in Universal Algebra by S. Burris,H. P. Sankappanavar Pdf

Universal algebra has enjoyed a particularly explosive growth in the last twenty years, and a student entering the subject now will find a bewildering amount of material to digest. This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests. Chapter I contains a brief but substantial introduction to lattices, and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence lattices is included. Chapter II develops the most general and fundamental notions of uni versal algebra-these include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems. Free algebras are discussed in great detail-we use them to derive the existence of simple algebras, the rules of equational logic, and the important Mal'cev conditions. We introduce the notion of classifying a variety by properties of (the lattices of) congruences on members of the variety. Also, the center of an algebra is defined and used to characterize modules (up to polynomial equivalence). In Chapter III we show how neatly two famous results-the refutation of Euler's conjecture on orthogonal Latin squares and Kleene's character ization of languages accepted by finite automata-can be presented using universal algebra. We predict that such "applied universal algebra" will become much more prominent.

Author : Stanley Burris,H. P. Sankappanavar
Publisher : Unknown
Page : 276 pages
File Size : 49,6 Mb
Release : 1981-01-01
Category : Algebra, Universal
ISBN : 3540905782

Get Book

A Course in Universal Algebra by Stanley Burris,H. P. Sankappanavar Pdf

Author : Clifford Bergman
Publisher : CRC Press
Page : 324 pages
File Size : 55,8 Mb
Release : 2011-09-20
Category : Computers
ISBN : 9781439851296

Get Book

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 : 41,7 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9783319114781

Get Book

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 : Dietlinde Lau
Publisher : Springer Science & Business Media
Page : 668 pages
File Size : 44,6 Mb
Release : 2006-11-23
Category : Mathematics
ISBN : 9783540360230

Get Book

Function Algebras on Finite Sets by Dietlinde Lau Pdf

Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.

Author : Stanley Burris
Publisher : Unknown
Page : 276 pages
File Size : 49,5 Mb
Release : 2012
Category : Electronic
ISBN : 0988055201

Get Book

A Course in Universal Algebra by Stanley Burris Pdf

Author : Jorge Almeida
Publisher : World Scientific
Page : 532 pages
File Size : 41,7 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 9789814501569

Get Book

Finite Semigroups and Universal Algebra by Jorge Almeida Pdf

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 AlgebraOrder and TopologyFinite AlgebrasDecidabilityFinite Semigroups and Monoids:PreliminariesPermutativityOperators Relating Semigroups and MonoidsSemigroups Whose Regular D-Classes are SubsemigroupsThe JoinThe Semidirect ProductThe PowerFactorization of Implicit OperationsOpen Problems Readership: Mathematicians and computer scientists. keywords:Inite Semigroups;Finite Monoids;Universal Algebra;Recognizable Languages;Pseudovarieties;Pseudoidentities;Implicit Operations;Relatively Free Profinite Semigroups;Semidirect Products;Power Semigroups “This book is devoted to an exciting new field where author has made important contributions, and thus it is a most welcome addition to the existing literature. It will find its place on the bookshelves of many a specialist in semigroups, as well as species of algebraists and computer scientists, including graduate students.” Semigroup Forum “The book … constitutes an important contribution to the most active part of the present theory of finite semigroups. All overwhelming majority of the results included in it is very new and has been scattered over journals so far. The book does not cover all of the theory of semigroup … but it is extremely rich in material and ideas presented with skill and dedication. The book has already influenced the area essentially, and its influence will certainly grow … I think the book is a must for researchers in the area but it is also very useful for all those who want to trace modern developments in the theory of semigroups.” Mathematics Abstracts

Author : Richard S Pierce
Publisher : Courier Corporation
Page : 162 pages
File Size : 54,7 Mb
Release : 2015-01-21
Category : Mathematics
ISBN : 9780486789989

Get Book

Introduction to the Theory of Abstract Algebras by Richard S Pierce Pdf

"Suitable for introductory graduate-level courses and independent study, this text presents the basic definitions of the theory of abstract algebra. Following introductory material, each of four chapters focuses on a major theme of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebra. Problems and a bibliography supplement the text. "--

Author : Hajnal Andréka,Zalán Gyenis,István Németi,Ildikó Sain
Publisher : Springer Nature
Page : 337 pages
File Size : 53,7 Mb
Release : 2022-11-01
Category : Mathematics
ISBN : 9783031148873

Get Book

Universal Algebraic Logic by Hajnal Andréka,Zalán Gyenis,István Németi,Ildikó Sain Pdf

This book gives a comprehensive introduction to Universal Algebraic Logic. The three main themes are (i) universal logic and the question of what logic is, (ii) duality theories between the world of logics and the world of algebra, and (iii) Tarskian algebraic logic proper including algebras of relations of various ranks, cylindric algebras, relation algebras, polyadic algebras and other kinds of algebras of logic. One of the strengths of our approach is that it is directly applicable to a wide range of logics including not only propositional logics but also e.g. classical first order logic and other quantifier logics. Following the Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually spacetime geometry leading up to relativity are also part of the perspective of the book. Besides Tarskian algebraizations of logics, category theoretical perspectives are also touched upon. This book, apart from being a monograph containing state of the art results in algebraic logic, can be used as the basis for a number of different courses intended for both novices and more experienced students of logic, mathematics, or philosophy. For instance, the first two chapters can be used in their own right as a crash course in Universal Algebra.

Author : Ralph Freese,Ralph McKenzie
Publisher : CUP Archive
Page : 244 pages
File Size : 43,8 Mb
Release : 1987-08-20
Category : Mathematics
ISBN : 0521348323

Get Book

Commutator Theory for Congruence Modular Varieties by Ralph Freese,Ralph McKenzie Pdf

Author : Ralph McKenzie,George F. McNulty,Walter Taylor
Publisher : Unknown
Page : 392 pages
File Size : 43,7 Mb
Release : 1987
Category : Algebra
ISBN : UOM:39015015615258

Get Book

Algebras, Lattices, Varieties by Ralph McKenzie,George F. McNulty,Walter Taylor Pdf

Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 41,5 Mb
Release : 1999-09
Category : Mathematics
ISBN : 0226511839

Get Book

A Concise Course in Algebraic Topology by J. P. May Pdf

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Author : Robin Hirsch,Ian Hodkinson
Publisher : Gulf Professional Publishing
Page : 722 pages
File Size : 41,9 Mb
Release : 2002-08-15
Category : Mathematics
ISBN : 0444509321

Get Book

Relation Algebras by Games by Robin Hirsch,Ian Hodkinson Pdf

In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises. P The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given.-

Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 44,8 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9780486820804

Get Book

Category Theory in Context by Emily Riehl Pdf

Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Author : Ėrnest Borisovich Vinberg
Publisher : American Mathematical Soc.
Page : 526 pages
File Size : 43,6 Mb
Release : 2003
Category : Algebra
ISBN : 9780821833186

Get Book

A Course in Algebra by Ėrnest Borisovich Vinberg Pdf

Great book! The author's teaching experinece shows in every chapter. --Efim Zelmanov, University of California, San Diego Vinberg has written an algebra book that is excellent, both as a classroom text or for self-study. It is plain that years of teaching abstract algebra have enabled him to say the right thing at the right time. --Irving Kaplansky, MSRI This is a comprehensive text on modern algebra written for advanced undergraduate and basic graduate algebra classes. The book is based on courses taught by the author at the Mechanics and Mathematics Department of Moscow State University and at the Mathematical College of the Independent University of Moscow. The unique feature of the book is that it contains almost no technically difficult proofs. Following his point of view on mathematics, the author tried, whenever possible, to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects. Another important feature is that the book presents most of the topics on several levels, allowing the student to move smoothly from initial acquaintance to thorough study and deeper understanding of the subject. Presented are basic topics in algebra such as algebraic structures, linear algebra, polynomials, groups, as well as more advanced topics like affine and projective spaces, tensor algebra, Galois theory, Lie groups, associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. Written with extreme care and supplied with more than 200 exercises and 70 figures, the book is also an excellent text for independent study.