Format:
1 online resource (xiv, 453 pages)
Edition:
Revised edition
ISBN:
9780521566742
,
9780511608681
Series Statement:
Cambridge studies in advanced mathematics 39
Content:
In the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. A separate chapter is devoted to Hilbert functions (including Macaulay's theorem) and numerical invariants derived from them. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. So the general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. Their connections with combinatorics are highlighted, e.g. Stanley's upper bound theorem or Ehrhart's reciprocity law for rational polytopes. The final chapters are devoted to Hochster's theorem on big Cohen-Macaulay modules and its applications, including Peskine-Szpiro's intersection theorem, the Evans-Griffith syzygy theorem, bounds for Bass numbers, and tight closure. Throughout each chapter the authors have supplied many examples and exercises which, combined with the expository style, will make the book very useful for graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for researchers in commutative algebra.
Content:
Regular sequences and depth -- Cohen-Macaulay rings -- The canonical module. Gorenstein rings -- Hilbert functions and multiplicities -- Stanley-Reisner rings -- Semigroup rings and invariant theory -- Determinantal rings -- Big Cohen-Macaulay modules -- Homological theorems -- Tight closure -- Appendix: A summary of dimension theory
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521566742
Additional Edition:
ISBN 9780521566742
Additional Edition:
Erscheint auch als Druck-Ausgabe Bruns, Winfried, 1946 - Cohen-Macaulay rings Cambridge [u.a.] : Cambridge Univ. Press, 1998 ISBN 0521566746
Additional Edition:
ISBN 0521410681
Language:
English
Subjects:
Mathematics
Keywords:
Lokale Kohomologie
;
Simpliziale Homologie
;
Cohen-Macaulay-Ring
;
Cohen-Macaulay-Modul
;
Halbgruppenring
;
Polytop
;
Simplizialer Komplex
;
Cohen-Macaulay-Ring
;
Darstellungstheorie
;
Invariantentheorie
;
Cohen-Macaulay-Ring
DOI:
10.1017/CBO9780511608681
Author information:
Herzog, Jürgen 1941-2024
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