Overview
- Authors:
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Frank W. Anderson
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Department of Mathematics, University of Oregon, Eugene, USA
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Kent R. Fuller
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Division of Mathematical Sciences, The University of Iowa, Iowa City, USA
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Table of contents (8 chapters)
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- Frank W. Anderson, Kent R. Fuller
Pages 1-9
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- Frank W. Anderson, Kent R. Fuller
Pages 10-64
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- Frank W. Anderson, Kent R. Fuller
Pages 65-114
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- Frank W. Anderson, Kent R. Fuller
Pages 115-149
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- Frank W. Anderson, Kent R. Fuller
Pages 150-176
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- Frank W. Anderson, Kent R. Fuller
Pages 177-249
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- Frank W. Anderson, Kent R. Fuller
Pages 250-287
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- Frank W. Anderson, Kent R. Fuller
Pages 288-326
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Back Matter
Pages 327-339
About this book
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-Art in Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semiperfect and perfect rings. 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. For example, we have made no attempt to cover such subjects as homology, rings of quotients, or commutative ring theory.
Authors and Affiliations
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Department of Mathematics, University of Oregon, Eugene, USA
Frank W. Anderson
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Division of Mathematical Sciences, The University of Iowa, Iowa City, USA
Kent R. Fuller