Cohen-Macaulay Rings 2ed - Couverture souple

Bruns/Herzog

 
9780521566742: Cohen-Macaulay Rings 2ed
Couverture souple
ISBN 10 : 0521566746 ISBN 13 : 9780521566742
Editeur : Cambridge University Press, 2008

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

' ... a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen–Macaulay rings ... very useful for graduate courses in algebra. As the only modern, broad account of the subject, it will be essential reading for specialists as well.' L'Enseignement Mathématique

'This book presents basic results in commutative algebra together with their applications in different special fields. It can be read immediately after an introductory text, but it brings you quickly to the main problems of the topic ... A lot of useful informations are packed also in the exercises which follow each section and in the notes which follow each chapter.' Zentralblatt für Mathematik

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2008
Langue
anglais
ISBN 10 
0521566746
ISBN 13 
9780521566742
Reliure
Broché
Numéro d'édition
2
Nombre de pages
468
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

chemin des peupliers 27
Dardilly
France

Autres éditions populaires du même titre

9780521410687: Cohen-Macaulay Rings

Edition présentée

ISBN 10 :  0521410681 ISBN 13 :  9780521410687
Editeur : Cambridge University Press, 1993
Couverture rigide