Rings and Categories of Modules

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Springer Science & Business Media, Sep 10, 1992 - Mathematics - 376 pages
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This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.
  

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Contents

II
1
III
10
V
26
VI
42
VII
55
VIII
65
X
78
XI
95
XXV
204
XXVI
218
XXVII
234
XXVIII
250
XXX
262
XXXI
269
XXXII
278
XXXIII
288

XII
105
XIII
115
XV
123
XVI
133
XVII
140
XVIII
150
XX
157
XXI
165
XXII
177
XXIII
178
XXIV
191
XXXIV
295
XXXV
301
XXXVI
312
XXXVII
322
XXXVIII
327
XL
336
XLI
345
XLII
363
XLIII
369
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About the author (1992)

Kent R. Fuller is a professor of mathematics at the University of Iowa. He is the author or coauthor of more than 70 research papers in ring and module theory, a dozen of which are joint work with Robert R. Colby. He is also coauthor of the widely known Rings and Categories of Modules. He has lectured on his research in several countries and is a member of the editorial board of the Journal of Algebra and belongs to the American Mathematical Society.

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