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Lectures in Universal Algebra

2016-01-22 Mathematics
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Release : 2016-01-22
Genre : Mathematics
Kind : eBook
Book Rating : 400/5 ( reviews)

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Book Synopsis Lectures in Universal Algebra by : L. Szabó

Download or read book Lectures in Universal Algebra written by L. Szabó. This book was released on 2016-01-22. Available in PDF, EPUB and Kindle. Book excerpt: These 34 papers cover topics ranging from various problems on varieties and other classes of algebras including categorical aspects and duality theory to the structure of finite algebras and clones on finite (or infinite) sets.As well as survey articles by invited speakers, the papers contain full proofs of new results not published elsewhere. The volume ends with a list of problems.

A Course in Universal Algebra

2011-10-21 Mathematics
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Release : 2011-10-21
Genre : Mathematics
Kind : eBook
Book Rating : 327/5 ( reviews)

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Book Synopsis A Course in Universal Algebra by : S. Burris

Download or read book A Course in Universal Algebra written by S. Burris. This book was released on 2011-10-21. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures in General Algebra

2014-07-10 Mathematics
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Release : 2014-07-10
Genre : Mathematics
Kind : eBook
Book Rating : 579/5 ( reviews)

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Book Synopsis Lectures in General Algebra by : A. G. Kurosh

Download or read book Lectures in General Algebra written by A. G. Kurosh. This book was released on 2014-07-10. Available in PDF, EPUB and Kindle. Book excerpt: Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.

Special Topics in Algebra, Universal Algebra

1962 Algebra, Universal
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Release : 1962
Genre : Algebra, Universal
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Special Topics in Algebra, Universal Algebra by : Bernhard Hermann Neumann

Download or read book Special Topics in Algebra, Universal Algebra written by Bernhard Hermann Neumann. This book was released on 1962. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures in Abstract Algebra I

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 018/5 ( reviews)

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Book Synopsis Lectures in Abstract Algebra I by : N. Jacobson

Download or read book Lectures in Abstract Algebra I written by N. Jacobson. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the first of three that will be published under the general title Lectures in Abstract Algebra. These vol umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale "University. The general plan of the work IS as follows: The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraIc concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond the foundations and elementary properties of the algebraic sys tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under standing of a few topics is to be preferred to a superficial under standing of many. The second and third volumes of this work will be more special ized in nature and will attempt to give comprehensive accounts of the topics which they treat. Volume II will bear the title Linear Algebra and will deal with the theorv of vectQ!_JlP. -a. ces. . . . . Volume III, The Theory of Fields and Galois Theory, will be con cerned with the algebraic structure offieras and with valuations of fields. All three volumes have been planned as texts for courses.

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