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Rings and Categories of Modules

  • Frank W. Anderson
  • Kent R. Fuller

Part of the Graduate Texts in Mathematics book series (GTM, volume 13)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Frank W. Anderson, Kent R. Fuller
    Pages 1-9
  3. Frank W. Anderson, Kent R. Fuller
    Pages 10-64
  4. Frank W. Anderson, Kent R. Fuller
    Pages 65-114
  5. Frank W. Anderson, Kent R. Fuller
    Pages 115-149
  6. Frank W. Anderson, Kent R. Fuller
    Pages 150-176
  7. Frank W. Anderson, Kent R. Fuller
    Pages 177-249
  8. Frank W. Anderson, Kent R. Fuller
    Pages 250-287
  9. Frank W. Anderson, Kent R. Fuller
    Pages 288-326
  10. Frank W. Anderson, Kent R. Fuller
    Pages 327-361
  11. Back Matter
    Pages 363-378

About this book

Introduction

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.

Keywords

algebra homomorphism representation theory ring transformation

Authors and affiliations

  • Frank W. Anderson
    • 1
  • Kent R. Fuller
    • 2
  1. 1.Department of MathematicsUniversity of OregonEugeneUSA
  2. 2.Department of MathematicsUniversity of IowaIowa CityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4418-9
  • Copyright Information Springer-Verlag New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8763-6
  • Online ISBN 978-1-4612-4418-9
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site