A Course In Universal Algebra

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A Course In Universal Algebra

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Author : S. Burris
language : en
Publisher: Springer
Release Date : 2011-10-21

A Course In Universal Algebra written by S. Burris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-21 with Mathematics categories.

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.

Universal Algebra

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Author : Clifford Bergman
language : en
Publisher: CRC Press
Release Date : 2011-09-20

Universal Algebra written by Clifford Bergman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-20 with Computers categories.

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

Finite Semigroups And Universal Algebra

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Author : Jorge Almeida
language : en
Publisher: World Scientific
Release Date : 1995-01-27

Finite Semigroups And Universal Algebra written by Jorge Almeida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-27 with Mathematics categories.

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.

Function Algebras On Finite Sets

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Author : Dietlinde Lau
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-23

Function Algebras On Finite Sets written by Dietlinde Lau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-23 with Mathematics categories.

Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied. This book gives a broad introduction to the theory of function algebras and leads to the cutting edge of research. To familiarize the reader from the very beginning on with the algebraic side of function algebras the more general concepts of the Universal Algebra is given in the first part of the book. The second part on fuction algebras covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, clone theory. This book is an insdispensible source on function algebras for graduate students and researchers in mathematical logic and theoretical computer science.

An Invitation To General Algebra And Universal Constructions

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Author : George M. Bergman
language : en
Publisher: Springer
Release Date : 2015-02-05

An Invitation To General Algebra And Universal Constructions written by George M. Bergman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-05 with Mathematics categories.

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.

A Course In Universal Algebra

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Author : Stanley Burris
language : en
Publisher: Springer
Release Date : 1981-11-16

A Course In Universal Algebra written by Stanley Burris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-11-16 with Mathematics categories.

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.

Proof Theory And Algebra In Logic

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Author : Hiroakira Ono
language : en
Publisher: Springer
Release Date : 2019-08-02

Proof Theory And Algebra In Logic written by Hiroakira Ono and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-02 with Philosophy categories.

This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.

Introduction To The Theory Of Abstract Algebras

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Author : Richard S Pierce
language : en
Publisher: Courier Corporation
Release Date : 2014-10-20

Introduction To The Theory Of Abstract Algebras written by Richard S Pierce and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-20 with Mathematics categories.

Suitable for introductory graduate-level courses and independent study, this text explores major themes of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebras. Includes problems and a bibliography. 1968 edition.

Abstract Algebra

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Author : Paul B. Garrett
language : en
Publisher: CRC Press
Release Date : 2007-09-25

Abstract Algebra written by Paul B. Garrett and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-25 with Mathematics categories.

Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal mapping properties, rather than by constructions whose technical details are irrelevant. Addresses Common Curricular Weaknesses In addition to standard introductory material on the subject, such as Lagrange's and Sylow's theorems in group theory, the text provides important specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. The book also focuses on broader background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, quadratic reciprocity, Dirichlet's theorem on primes in arithmetic progressions, and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.

An Algebraic Introduction To K Theory

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Author : Bruce A. Magurn
language : en
Publisher: Cambridge University Press
Release Date : 2002-05-20

An Algebraic Introduction To K Theory written by Bruce A. Magurn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-20 with Mathematics categories.

This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.