Graduate Texts in Mathematics

Rings and Categories of Modules

Authors: Anderson, Frank W., Fuller, Kent R.

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About this Textbook

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 familĀ­ 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, deĀ­ 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.

Table of contents (9 chapters)

  • Preliminaries

    Anderson, Frank W. (et al.)

    Pages 1-9

  • Rings, Modules and Homomorphisms

    Anderson, Frank W. (et al.)

    Pages 10-64

  • Direct Sums and Products

    Anderson, Frank W. (et al.)

    Pages 65-114

  • Finiteness Conditions for Modules

    Anderson, Frank W. (et al.)

    Pages 115-149

  • Classical Ring-Structure Theorems

    Anderson, Frank W. (et al.)

    Pages 150-176

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4612-4418-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $95.00
price for USA
  • ISBN 978-0-387-97845-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $95.00
price for USA
  • ISBN 978-1-4612-8763-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Rings and Categories of Modules
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
13
Copyright
1992
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4612-4418-9
DOI
10.1007/978-1-4612-4418-9
Hardcover ISBN
978-0-387-97845-1
Softcover ISBN
978-1-4612-8763-6
Series ISSN
0072-5285
Edition Number
2
Number of Pages
X, 378
Topics