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Author Christensen, Lars Winther, 1969-

Title Gorenstein dimensions [electronic resource] / Lars Winther Christensen.

Published Berlin ; New York : Springer, ò000.


Location Call No. Status
Physical description 1 online resource (viii, 204 pages).
Series Lecture notes in mathematics, 0075-8434 ; 1747
Lecture notes in mathematics (Springer-Verlag) ; 1747.
Bibliography Includes bibliographical references (p. [191]-195) and index.
Contents Introduction -- Synopsis -- Conventions and prerequisites -- The classical Gorenstein dimension -- G-dimension and reflexive complexes -- Auslander categories -- G-projectivity. -- G-injectivity -- Appendix: Hyperhomology. Basic definitions and notation. Standard functors and morphisms. Resolutions. Almost derived functors. Homological dimensions. Depth and width. Numerical and formal invariants. Dualizing complexes.
Summary 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.
Subject Gorenstein rings.
Homology theory.
Gorenstein rings.
Homology theory.
Electronic books.
ISBN 9783540400080 (electronic bk.)
3540400087 (electronic bk.)