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  • © 1993

Gröbner Bases

A Computational Approach to Commutative Algebra

Part of the book series: Graduate Texts in Mathematics (GTM, volume 141)

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  • ISBN: 978-1-4612-0913-3
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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxii
  2. Basics

    • Thomas Becker, Volker Weispfenning
    Pages 1-13
  3. Commutative Rings with Unity

    • Thomas Becker, Volker Weispfenning
    Pages 15-59
  4. Polynomial Rings

    • Thomas Becker, Volker Weispfenning
    Pages 61-118
  5. Vector Spaces and Modules

    • Thomas Becker, Volker Weispfenning
    Pages 119-139
  6. Orders and Abstract Reduction Relations

    • Thomas Becker, Volker Weispfenning
    Pages 141-185
  7. Gröbner Bases

    • Thomas Becker, Volker Weispfenning
    Pages 187-242
  8. First Applications of Gröbner Bases

    • Thomas Becker, Volker Weispfenning
    Pages 243-292
  9. Field Extensions and the Hilbert Nullstellensatz

    • Thomas Becker, Volker Weispfenning
    Pages 293-333
  10. Decomposition, Radical, and Zeroes of Ideals

    • Thomas Becker, Volker Weispfenning
    Pages 335-421
  11. Linear Algebra in Residue Class Rings

    • Thomas Becker, Volker Weispfenning
    Pages 423-452
  12. Variations on Gröbner Bases

    • Thomas Becker, Volker Weispfenning
    Pages 453-509
  13. Back Matter

    Pages 511-576

About this book

The origins of the mathematics in this book date back more than two thou­ sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu­ clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek­ istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al­ gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.

Keywords

  • Abstract algebra
  • Algebra
  • Algebraic structure
  • Finite
  • Morphism
  • Vector space
  • axiom of choice
  • equation
  • function
  • mathematics
  • theorem

Authors and Affiliations

  • Fakultät für Mathematik und Informatik Universität Passau, Passau, Germany

    Thomas Becker, Volker Weispfenning

Bibliographic Information

  • Book Title: Gröbner Bases

  • Book Subtitle: A Computational Approach to Commutative Algebra

  • Authors: Thomas Becker, Volker Weispfenning

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0913-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1993

  • Hardcover ISBN: 978-0-387-97971-7

  • Softcover ISBN: 978-1-4612-6944-1

  • eBook ISBN: 978-1-4612-0913-3

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XXII, 576

  • Topics: Group Theory and Generalizations, Algebra

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-0913-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 99.99
Price excludes VAT (USA)
Hardcover Book USD 119.99
Price excludes VAT (USA)