Local Algebra by Jean-Pierre Serre

Local Algebra by Jean-Pierre Serre

Local Algebra by Jean-Pierre Serre – Translated from the French by CheeWhye Chin

Contents of Local Algebra eBook

  • Prime Ideals and Localization
  • Tools
  • Dimension Theory
  • Homological Dimension and Depth
  • Multiplicities

This book is an English translation of Algebra – Multiples published by Springer-Verlag as no. 11 of the Lecture Notes series. The original text was based on a collection of lectures given at the Collège de France in 1957-1958, written by Pierre Gabriel.

Its aim was to provide a short account of commutative algebra, focusing on the following topics: a) units (as opposed to rings, which were thought to be the only subject of commutative algebra, before the emergence of sheave theory in the 1950s); b) Homological methods, similar to Cartan-Eilenberg; c) The multiplicity of intersections, seen as the Euler-Poincaré properties.

The English translation, made with great care by Chee Whye Chin, differs from the original translation in the following respects.

The terminology has been updated (for example, the “common dimension” has been replaced by the now usual “depth”). I’ve rewrote some proofs and clarified (or so I hope) more.

A section on Gradient Algebra (App. III to Chap. IV) has been added.

New references have been given, especially to other books on social algebra: Bourbaki (whose chapter 10 has now appeared, after a 40-year wait), Eisenbaud, Matsumura, Roberts, … I hope that these changes will make the text easier to read, without Change its informal character to Lecture Notes.

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