Algebra Ii Ring Theory
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Algebra Ii Ring Theory
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Author : Carl Faith
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebra Ii Ring Theory written by Carl Faith 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 2012-12-06 with Mathematics categories.
Algebra Ii
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Author : A.I. Kostrikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebra Ii written by A.I. Kostrikin 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 2012-12-06 with Mathematics categories.
The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge 1 bra • Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le.
The Theory Of Rings
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Author : Nathan Jacobson
language : en
Publisher: American Mathematical Soc.
Release Date : 1943-12-31
The Theory Of Rings written by Nathan Jacobson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1943-12-31 with Mathematics categories.
The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.
Ring Theory Ii
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Author : Bernard R. McDonald
language : en
Publisher:
Release Date : 1977
Ring Theory Ii written by Bernard R. McDonald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.
Commutative Ring Theory
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Author : Paul-Jean Cahen
language : en
Publisher: CRC Press
Release Date : 2023-06-14
Commutative Ring Theory written by Paul-Jean Cahen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-14 with Mathematics categories.
Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.
Exercises In Classical Ring Theory
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-09
Exercises In Classical Ring Theory written by T.Y. Lam 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 2006-05-09 with Mathematics categories.
" This useful book, which grew out of the author's lectures at Berkeley, presents some 400 exercises of varying degrees of difficulty in classical ring theory, together with complete solutions, background information, historical commentary, bibliographic details, and indications of possible improvements or generalizations. The book should be especially helpful to graduate students as a model of the problem-solving process and an illustration of the applications of different theorems in ring theory. The author also discusses "the folklore of the subject: the 'tricks of the trade' in ring theory, which are well known to the experts in the field but may not be familiar to others, and for which there is usually no good reference". The problems are from the following areas: the Wedderburn-Artin theory of semisimple rings, the Jacobson radical, representation theory of groups and algebras, (semi)prime rings, (semi)primitive rings, division rings, ordered rings, (semi)local rings, the theory of idempotents, and (semi)perfect rings. Problems in the areas of module theory, category theory, and rings of quotients are not included, since they will appear in a later book. " (T. W. Hungerford, Mathematical Reviews)
Commutative Algebra Ii
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Author : O. Zariski
language : en
Publisher: Springer Science & Business Media
Release Date : 1976-03-29
Commutative Algebra Ii written by O. Zariski 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 1976-03-29 with Mathematics categories.
From the Preface: "topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); (c) local algebra... the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered throughout the exposition. Thus, this volume can be used in part as an introduction to some basic concepts and the arithmetic foundations of algebraic geometry."
Abstract Algebra With Applications
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Author : Karlheinz Spindler
language : en
Publisher: CRC Press
Release Date : 1993-10-18
Abstract Algebra With Applications written by Karlheinz Spindler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-18 with Mathematics categories.
A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Advances In Ring Theory
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Author : Sergio R. López-Permouth
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-28
Advances In Ring Theory written by Sergio R. López-Permouth 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 2011-01-28 with Mathematics categories.
This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra.
Ring Theory 83
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Author : Louis H. Rowen
language : en
Publisher: Academic Press
Release Date : 2012-12-02
Ring Theory 83 written by Louis H. Rowen and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**"As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of nonexperts, mathematicians whose speciality is not ring theory, will find Ring Theory ideally suited to their needs....They, as well as students, will be well served by the many examples of rings and the glossary of major results."**--NOTICES OF THE AMS