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Commutative Algebra

with a View Toward Algebraic Geometry

  • David Eisenbud

Part of the Graduate Texts in Mathematics book series (GTM, volume 150)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Introduction

    1. David Eisenbud
      Pages 1-10
  3. Elementary Definitions

    1. David Eisenbud
      Pages 11-17
  4. Basic Constructions

    1. Front Matter
      Pages 19-19
    2. David Eisenbud
      Pages 21-56
    3. David Eisenbud
      Pages 57-86
    4. David Eisenbud
      Pages 87-115
    5. David Eisenbud
      Pages 117-144
    6. David Eisenbud
      Pages 145-153
    7. David Eisenbud
      Pages 155-178
    8. David Eisenbud
      Pages 179-209
  5. Dimension Theory

    1. Front Matter
      Pages 211-211
    2. David Eisenbud
      Pages 213-224
    3. David Eisenbud
      Pages 225-229
    4. David Eisenbud
      Pages 247-269
    5. David Eisenbud
      Pages 271-280
    6. David Eisenbud
      Pages 281-301
    7. David Eisenbud
      Pages 317-381
    8. David Eisenbud
      Pages 383-415
  6. Homological Methods

    1. Front Matter
      Pages 417-417
    2. David Eisenbud
      Pages 419-446
    3. David Eisenbud
      Pages 447-468
    4. David Eisenbud
      Pages 469-488
    5. David Eisenbud
      Pages 489-517
  7. Back Matter
    Pages 555-788

About this book

Introduction

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.

Keywords

Algebraic Geometry algebra algebraic geometry category theory cohomology colimit commutative algebra Dimension field homological algebra linear algebra polynomial

Authors and affiliations

  • David Eisenbud
    • 1
  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5350-1
  • Copyright Information Springer-Verlag New York 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-78122-6
  • Online ISBN 978-1-4612-5350-1
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site