A Singular Introduction to Commutative Algebra

  • Gert-Martin Greuel
  • Gerhard Pfister

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Gert-Martin Greuel, Gerhard Pfister
    Pages 1-88
  3. Gert-Martin Greuel, Gerhard Pfister
    Pages 89-190
  4. Gert-Martin Greuel, Gerhard Pfister
    Pages 191-237
  5. Gert-Martin Greuel, Gerhard Pfister
    Pages 239-274
  6. Gert-Martin Greuel, Gerhard Pfister
    Pages 275-312
  7. Gert-Martin Greuel, Gerhard Pfister
    Pages 313-334
  8. Gert-Martin Greuel, Gerhard Pfister
    Pages 335-399
  9. Back Matter
    Pages 401-588

About this book


This book can be understood as a model for teaching commutative algebra, taking into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, it is shown how to handle it by computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The text starts with the theory of rings and modules and standard bases with emphasis on local rings and localization. It is followed by the central concepts of commutative algebra such as integral closure, dimension theory, primary decomposition, Hilbert function, completion, flatness and homological algebra. There is a substantial appendix about algebraic geometry in order to explain how commutative algebra and computer algebra can be used for a better understanding of geometric problems. The book includes a CD with a distribution of Singular for various platforms (Unix/Linux, Windows, Macintosh), including all examples and procedures explained in the book. The book can be used for courses, seminars and as a basis for studying research papers in commutative algebra, computer algebra and algebraic geometry.


algebra algebraic geometry algebraic varieties algorithms commutative algebra computer algebra geometry homomorphism

Authors and affiliations

  • Gert-Martin Greuel
    • 1
  • Gerhard Pfister
    • 1
  1. 1.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-42897-8
  • Online ISBN 978-3-662-04963-1
  • Buy this book on publisher's site