Bibliographic Information

Cohen-Macaulay rings

Winfried Bruns, Jürgen Herzog

(Cambridge studies in advanced mathematics, 39)

Cambridge University Press, 1998, c1993

1st pbk ed. with revisions

  • : pbk

Available at  / 47 libraries

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Note

Includes bibliographical references (p. 420-438) and index

"Transferred to digital printing 2005"--T.p. verso

Description and Table of Contents

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 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.

Table of Contents

  • 1. Regular sequences and depth
  • 2. Cohen-Macaulay rings
  • 3. The canonical module. Gorenstein rings
  • 4. Hilbert functions and multiplicities
  • 5. Stanley-Reisner rings
  • 6. Semigroup rings and invariant theory
  • 7. Determinantal rings
  • 8. Big Cohen-Macaulay modules
  • 9. Homological theorems
  • 10. Tight closure.

by "Nielsen BookData"

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Details

  • NCID
    BA36884647
  • ISBN
    • 9780521566742
  • LCCN
    93016069
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge [England]
  • Pages/Volumes
    xiv, 453 p.
  • Size
    23 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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