Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Cohen-Macaulay Rings
  • Cited by 629
      • 2nd edition
      • You may already have access via personal or institutional login
    • Select format
    • Publisher:
      Cambridge University Press
      Publication date:
      04 December 2009
      18 June 1998
      ISBN:
      9780511608681
      9780521566742
      DOI:
      https://doi.org/10.1017/CBO9780511608681
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.633kg, 468 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      Cambridge Studies in Advanced Mathematics (39)
    You may already have access via personal or institutional login
    • Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Cambridge Studies in Advanced Mathematics (39)
    Information

    Book 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.

    Reviews

    ‘ … 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.’

    Source: 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.’

    Source: Zentralblatt für Mathematik

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    Contents

    Contents

    Metrics

    Altmetric attention score

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.