Local Algebra

  • Jean-Pierre Serre

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jean-Pierre Serre
    Pages 1-10
  3. Jean-Pierre Serre
    Pages 11-27
  4. Jean-Pierre Serre
    Pages 29-49
  5. Jean-Pierre Serre
    Pages 51-97
  6. Jean-Pierre Serre
    Pages 99-121
  7. Back Matter
    Pages 123-130

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original in the following aspects: - The terminology has been brought up to date (e.g. "cohomological dimension" has been replaced by the now customary "depth").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.


Tor-formula algebra commutative algebra intersection multilicity multiplicity

Authors and affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Collège de FranceParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04203-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08590-1
  • Online ISBN 978-3-662-04203-8
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book