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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-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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Table of contents (9 chapters)
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Front Matter
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Back Matter
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Bibliographic information
Book title: Rings and Categories of Modules
Authors: Frank W. Anderson, Kent R. Fuller
Series title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-4418-9
Publisher: Springer New York, NY
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eBook packages: Springer Book Archive
Copyright information: Springer-Verlag New York, Inc. 1992
Hardcover ISBN: 978-0-387-97845-1Published: 18 August 1998
Softcover ISBN: 978-1-4612-8763-6Published: 26 September 2011
eBook ISBN: 978-1-4612-4418-9Published: 06 December 2012
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition number: 2
Number of pages: X, 378
Topics: Algebra