Cohen-Macaulay Rings

Name: Cohen-Macaulay Rings
Availability: OutOfStock
ISBN: 9780521410687

ISBN-10: 0521410681

ISBN-13: 9780521410687

Edition: 1993

Authors: Winfried Bruns, Jï¿½rgen Herzog

List price: $125.99

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Description:

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…

Book details

List price: $125.99
Copyright year: 1993
Publisher: Cambridge University Press
Publication date: 11/4/1993
Binding: Hardcover
Pages: 415
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 1.540
Language: English



Preface



Regular sequences and depth



Regular sequences



Grade and depth



Depth and projective dimension



Some linear algebra



Graded rings and modules



The Koszul complex



Cohen-Macaulay rings



Cohen-Macaulay rings and modules



Regular rings and normal rings



Complete intersections



The canonical module. Gorenstein rings



Finite modules of finite injective dimension



Injective hulls. Matlis duality



The canonical module



Gorenstein ideals of grade 3. Poincare duality



Local cohomology. The local duality theorem



The canonical module of a graded ring



Hilbert functions and multiplicities



Hilbert functions of graded modules



Macaulay's theorem on Hilbert functions



Further constraints on Hilbert functions



Filtered rings



The Hilbert-Samuel function and reduction ideals



The multiplicity symbol



Stanley-Reisner rings



Simplicial complexes



Polytopes



Local cohomology of Stanley-Reisner rings



The upper bound theorem



Gorenstein complexes



The canonical module of a Stanley-Reisner ring



Semigroup rings and invariant theory



Affine semigroup rings



Local cohomology of affine semigroup rings



Normal semigroup rings



Invariants of tori and finite groups



Invariants of linearly reductive groups



Determinantal rings



Graded Hodge algebras



Straightening laws on posets of minors



Properties of determinantal rings



Big Cohen-Macaulay modules



The annihilators of local cohomology



The Frobenius functor



Modifications and non-degeneracy



Hochster's finiteness theorem



Balanced big Cohen-Macaulay modules



Homological theorems



Grade and acyclicity



Regular rings as direct summands



Canonical elements in local cohomology modules



Intersection theorems



Ranks of syzygies



Bass numbers


Appendix: A summary of dimension theory


References


Notation


Index