Gorenstein Dimensions

Lars Winther Christensen (auth.)9783540411321, 3540411321

This book is intended as a reference for mathematicians working with homological dimensions in commutative algebra and as an introduction to Gorenstein dimensions for graduate students with an interest in the same. Any admirer of classics like the Auslander-Buchsbaum-Serre characterization of regular rings, and the Bass and Auslander-Buchsbaum formulas for injective and projective dimension of f.g. modules will be intrigued by this book’s content.
Readers should be well-versed in commutative algebra and standard applications of homological methods. The framework is that of complexes, but all major results are restated for modules in traditional notation, and an appendix makes the proofs accessible for even the casual user of hyperhomological methods.

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Table of contents :
Front Matter….Pages –
Introduction….Pages 1-2
Synopsis….Pages 3-8
Conventions and prerequisites….Pages 9-15
The classical Gorenstein dimension….Pages 17-40
G-dimension and reflexive complexes….Pages 41-63
Auslander categories….Pages 65-90
G-projectivity….Pages 91-112
G-flatness….Pages 113-134
G-injectivity….Pages 135-158
Back Matter….Pages –