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. Back Matter
    Pages 327-339

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-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.

Keywords

Area Categories Division Finite Modules Rings algebra behavior density duality functions homomorphism ring theorem transformation

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9913-1
  • Copyright Information Springer-Verlag New York 1974
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90070-4
  • Online ISBN 978-1-4684-9913-1
  • Series Print ISSN 0072-5285
  • About this book