Gorenstein Dimensions

2000
ISBN: 978-3-540-41132-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1747, 210 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 338 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Christensen, Lars W.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.