Gorenstein Dimensions [electronic resource] / by Lars Winther Christensen.
Material type: TextSeries: Lecture Notes in Mathematics ; 1747Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2000Description: X, 210 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540400080Subject(s): Mathematics | K-theory | Mathematics | K-TheoryAdditional physical formats: Printed edition:: No titleDDC classification: 512.66 LOC classification: QA612.33Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1219 |
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.
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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