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Commutative Algebra

Volume II

  • Oscar Zariski
  • Pierre Samuel

Part of the Graduate Texts in Mathematics book series (GTM, volume 29)

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

Introduction

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.

Keywords

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 https://doi.org/10.1007/978-3-662-29244-0
  • 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