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Rings and Categories of Modules (Hardcover, 2nd ed. 1992)
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Rings and Categories of Modules (Hardcover, 2nd ed. 1992)
Series: Graduate Texts in Mathematics, 13
Expected to ship within 10 - 15 working days
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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."
General
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