Table of contents

  1. Front Matter
    Pages i-x
  2. Oscar Zariski, Pierre Samuel
    Pages 1-128
  3. Oscar Zariski, Pierre Samuel
    Pages 129-247
  4. Oscar Zariski, Pierre Samuel
    Pages 248-320
  5. Back Matter
    Pages 321-416

About this book


This second volume of our treatise on commutative algebra deals largely with three basic topics, which go beyond the more or less classical material of volume I and are on the whole of a more advanced nature and a more recent vintage. These topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); (c) local algebra. Because most of these topics have either their source or their best motivation in algebraic geom­ etry, the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered through­ out the exposition. Thus, this volume can be used in part as an introduc­ tion to some basic concepts and the arithmetic foundations of algebraic geometry. The reader who is not immediately concerned with geometric applications may omit the algebro-geometric material in a first reading (see" Instructions to the reader," page vii), but it is only fair to say that many a reader will find it more instructive to find out immediately what is the geometric motivation behind the purely algebraic material of this volume. The first 8 sections of Chapter VI (including § 5bis) deal directly with properties of places, rather than with those of the valuation associated with a place. These, therefore, are properties of valuations in which the value group of the valuation is not involved.


Grad algebra algebraic geometry commutative algebra polynomial

Authors and affiliations

  • Oscar Zariski
    • 1
  • Pierre Samuel
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Mathématique / Bâtiment 425Université de Paris-SudOrsayFrance

Bibliographic information

  • DOI
  • Copyright Information O. Zariski and P. Samuel 1960
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-27753-9
  • Online ISBN 978-3-662-29244-0
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site