Rings and Things and a Fine Array of Twentieth Century Associative Algebra

Rings and Things and a Fine Array of Twentieth Century Associative Algebra

by Carl Clifton Faith
     
 

ISBN-10: 0821809938

ISBN-13: 9780821809938

Pub. Date: 11/28/1998

Publisher: American Mathematical Society

This book surveys more than 125 years of aspects of associative algebras, especially ring and module theory. It is the first to probe so extensively such a wealth of historical development. Moreover, the author brings the reader up to date, in particular through his report on the subject in the second half of the twentieth century. In the second part of the book,

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Overview

This book surveys more than 125 years of aspects of associative algebras, especially ring and module theory. It is the first to probe so extensively such a wealth of historical development. Moreover, the author brings the reader up to date, in particular through his report on the subject in the second half of the twentieth century. In the second part of the book, the author gives descriptive impressions of the last half of the twentieth century. Beginning with his teachers and fellow graduate students at the University of Kentucky and at Purdue, Faith discusses his Fulbright-NATO Postdoctoral at Heidelberg and at the Institute for Advanced Study at Princeton, his year as a visiting scholar at Berkeley, and the many acquaintances he met there and in subsequent travels in India, Europe, and most recently, Barcelona.

Product Details

ISBN-13:
9780821809938
Publisher:
American Mathematical Society
Publication date:
11/28/1998
Series:
Mathematical Surveys and Monographs Series
Pages:
422

Related Subjects

Table of Contents

Symbols
Preface
Acknowledgements
Ch. 1Direct Product and Sums of Rings and Modules and the Structure of Fields1
Ch. 2Introduction to Ring Theory: Schur's Lemma and Semisimple Rings, Prime and Primitive Rings, Noetherian and Artinian Modules, Nil, Prime and Jacobson Radicals15
Ch. 3Direct Decompositions of Projective and Injective Modules51
Ch. 4Direct Product Decompositions of von Neumann Regular Rings and Self-injective Rings89
Ch. 5Direct Sums of Cyclic Modules105
Ch. 6When Injectives Are Flat: Coherent FP-injective Rings121
Ch. 7Direct Decompositions and Dual Generalizations of Noetherian Rings139
Ch. 8Completely Decomposable Modules and the Krull-Schmidt-Azumaya Theorem153
Ch. 9Polynomial Rings over Vamosian and Kerr Rings, Valuation Rings and Prufer Rings163
Ch. 10Isomorphic Polynomial Rings and Matrix Rings173
Ch. 11Group Rings and Maschke's Theorem Revisited175
Ch. 12Maximal Quotient Rings179
Ch. 13Morita Duality and Dual Rings193
Ch. 14Krull and Global Dimensions205
Ch. 15Polynomials Identities and PI-Rings221
Ch. 16Unions of Primes, Prime Avoidance, Associated Prime Ideals, Acc on Irreducible Ideals, and Annihilator Ideals in Commutative Rings229
Ch. 17Dedekind's Theorem on the Independence of Automorphisms Revisited243
Ch. 18Some Mathematical Friends and Places255
Bibliography325
Register of Names387
Index of Terms and Authors of Theorems395

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