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Author : Anna B. Romanowska,Jonathan D. H. Smith
Publisher : Unknown
Page : 258 pages
File Size : 53,9 Mb
Release : 1992
Category : Mathematics
ISBN : UOM:39015051268343
Author : Jonathan D. H. Smith
Publisher : CRC Press
Page : 353 pages
File Size : 41,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9781420010633
Collecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this extension. To fully understand representation theory,
Author : Clifford Bergman
Publisher : CRC Press
Page : 324 pages
File Size : 45,9 Mb
Release : 2011-09-20
Category : Computers
ISBN : 9781439851296
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 : Jonathan D. H. Smith,Anna B. Romanowska
Publisher : John Wiley & Sons
Page : 386 pages
File Size : 50,6 Mb
Release : 2011-09-30
Category : Mathematics
ISBN : 9781118030837
Advanced algebra in the service of contemporary mathematicalresearch-- a unique introduction. This volume takes an altogether new approach to advanced algebra.Its intriguing title, inspired by the term postmodernism, denotes adeparture from van der Waerden's Modern Algebra--a book that hasdominated the field for nearly seventy years. Post-Modern Algebraoffers a truly up-to-date alternative to the standard approach,explaining topics from an applications-based perspective ratherthan by abstract principles alone. The book broadens the field ofstudy to include algebraic structures and methods used in currentand emerging mathematical research, and describes the powerful yetsubtle techniques of universal algebra and category theory.Classical algebraic areas of groups, rings, fields, and vectorspaces are bolstered by such topics as ordered sets, monoids,monoid actions, quasigroups, loops, lattices, Boolean algebras,categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested inuniversity courses. * A wealth of exercises illustrating concepts and their practicalapplication. * Effective techniques for solving research problems in the realworld. * Flexibility of presentation, making it easy to tailor material tospecific needs. * Help with elementary proofs and algebraic notations for studentsof varying abilities. Post-Modern Algebra is an excellent primary or supplementary textfor graduate-level algebra courses. It is also an extremely usefulresource for professionals and researchers in many areas who musttackle abstract, linear, or universal algebra in the course oftheir work.
Author : R.S. Freese,O.C. Garcia
Publisher : Springer
Page : 314 pages
File Size : 55,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540409540
Author : Orin Chein,Hala O. Pflugfelder,Jonathan D. H. Smith
Publisher : Unknown
Page : 596 pages
File Size : 50,7 Mb
Release : 1990
Category : Loops (Group theory).
ISBN : UOM:39015019608390
Author : Valery B. Kudryavtsev,Ivo G. Rosenberg
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 55,8 Mb
Release : 2006-01-18
Category : Mathematics
ISBN : 9781402038174
Semigroups, Automata, Universal Algebra, Varieties
Author : Anonim
Publisher : Unknown
Page : 272 pages
File Size : 55,8 Mb
Release : 1994
Category : Group theory
ISBN : UOM:39015057355763
Author : Victor Shcherbacov
Publisher : CRC Press
Page : 576 pages
File Size : 53,6 Mb
Release : 2017-05-12
Category : Computers
ISBN : 9781498721561
This book provides an introduction to quasigroup theory along with new structural results on some of the quasigroup classes. Many results are presented with some of them from mathematicians of the former USSR. These included results have not been published before in the western mathematical literature. In addition, many of the achievements obtained with regard to applications of quasigroups in coding theory and cryptology are described.
Author : S. Burris,H. P. Sankappanavar
Publisher : Springer
Page : 276 pages
File Size : 50,6 Mb
Release : 2011-10-21
Category : Mathematics
ISBN : 1461381320
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 : Hanna Neumann
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642885990
Varieties of algebras are equationally defined classes of algebras, or "primitive classes" in MAL'CEV'S terminology. They made their first explicit appearance in the 1930's, in Garrett BIRKHOFF'S paper on "The structure of abstract algebras" and B. H. NEUMANN'S paper "Identical relations in groups I". For quite some time after this, there is little published evidence that the subject remained alive. In fact, however, as part of "universal algebra", it aroused great interest amongst those who had access, directly or indirectly, to PHILIP HALL'S lectures given at Cambridge late in the 1940's. More recently, category theory has provided a general setting since varieties, suitably interpreted, are very special examples of categories. Whether their relevance to category theory goes beyond this, I do not know. And I doubt that the category theoretical approach to varieties will be more than a fringe benefit to group theory. Whether or not my doubts have substance, the present volume owes its existence not to the fact that varieties fit into a vastly more general pattern, but to the benefit group theory has derived from the classification of groups by varietal properties. It is this aspect of the study of varieties that seems to have caused its reappearance in the literature in the 1950's.
Author : Stephen D. Comer
Publisher : Springer
Page : 290 pages
File Size : 52,8 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540396383
Author : Clifford Bergman
Publisher : CRC Press
Page : 320 pages
File Size : 49,8 Mb
Release : 2011-09-20
Category : Computers
ISBN : 9781000750584
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 o
Author : Janusz Czelakowski
Publisher : Springer
Page : 454 pages
File Size : 49,9 Mb
Release : 2018-03-20
Category : Philosophy
ISBN : 9783319747729
This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.
Author : B. Csákány,Jurgen Schmidt
Publisher : North-Holland
Page : 614 pages
File Size : 40,5 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:39015037744003
Contributions to Universal Algebra focuses on the study of algebra.
