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Local Algebra

  • Book
  • © 2000

Overview

Authors:
  1. Jean-Pierre Serre

    1. Collège de France, Paris, France

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Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Prime Ideals and Localization

    • Jean-Pierre Serre
    Pages 1-10

  3. Tools

    • Jean-Pierre Serre
    Pages 11-27

  4. Dimension Theory

    • Jean-Pierre Serre
    Pages 29-49

  5. Homological Dimension and Depth

    • Jean-Pierre Serre
    Pages 51-97

  6. Multiplicities

    • Jean-Pierre Serre
    Pages 99-121

  7. Back Matter

    Pages 123-130
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Keywords

About this book

The present book is an English translation of Algebre Locale - Multiplicites published by Springer-Verlag as no. 11 of the Lecture Notes series. The original text was based on a set of lectures, given at the College de France in 1957-1958, and written up by Pierre Gabriel. Its aim was to give a short account of Commutative Algebra, with emphasis on the following topics: a) Modules (as opposed to Rings, which were thought to be the only subject of Commutative Algebra, before the emergence of sheaf theory in the 1950s); b) H omological methods, a la Cartan-Eilenberg; c) Intersection multiplicities, viewed as Euler-Poincare characteristics. The English translation, done with great care by Chee Whye Chin, differs from the original in the following aspects: - The terminology has been brought up to date (e.g. "cohomological dimension" has been replaced by the now customary "depth"). I have rewritten a few proofs and clarified (or so I hope) a few more. - A section on graded algebras has been added (App. III to Chap. IV). - New references have been given, especially to other books on Commu- tive Algebra: Bourbaki (whose Chap. X has now appeared, after a 40-year wait) , Eisenbud, Matsumura, Roberts, .... I hope that these changes will make the text easier to read, without changing its informal "Lecture Notes" character.

Authors and Affiliations

  • Collège de France, Paris, France

    Jean-Pierre Serre

Bibliographic Information

  • Book Title: Local Algebra

  • Authors: Jean-Pierre Serre

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-04203-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Hardcover ISBN: 978-3-540-66641-7Published: 16 June 2000

  • Softcover ISBN: 978-3-642-08590-1Published: 13 August 2011

  • eBook ISBN: 978-3-662-04203-8Published: 06 December 2012

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XV, 130

  • Additional Information: Original French edition published as volume 11 in the series: Lecture Notes Mathematics, 1965

  • Topics: Algebra

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