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<図書>
Cohen-Macaulay rings

責任表示 Winfried Bruns, Jürgen Herzog
シリーズ Cambridge studies in advanced mathematics ; 39
データ種別 図書
出版者 Cambridge [England] : Cambridge University Press
出版年 1993
本文言語 英語
大きさ xi, 403 p. ; 24 cm
概要 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 co...binatorial 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, and bounds for Bass numbers. 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. 続きを見る

所蔵情報


理系図3F 数理独自 068222193004693 BRUN/50/1 1993

書誌詳細

一般注記 Includes bibliographical references and index
著者標目 *Bruns, Winfried, 1946-
Herzog, Jürgen
件 名 LCSH:Cohen-Macaulay rings
分 類 LCC:QA251.38
DC20:512/.4
書誌ID 1000036074
ISBN 0521410681
NCID BA21036043
巻冊次 ISBN:0521410681
登録日 2009.09.10
更新日 2009.11.02

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