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Number Fields

  • Textbook
  • © 1977

Overview

Authors:
  1. Daniel A. Marcus

    1. Department of Mathematics, California State Polytechnic University, Pomona, USA

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Part of the book series: Universitext (UTX)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
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  2. A special case of Fermat’s conjecture

    • Daniel A. Marcus
    Pages 1-11

  3. Number fields and number rings

    • Daniel A. Marcus
    Pages 12-54

  4. Prime decomposition in number rings

    • Daniel A. Marcus
    Pages 55-97

  5. Galois theory applied to prime decomposition

    • Daniel A. Marcus
    Pages 98-129

  6. The ideal class group and the unit group

    • Daniel A. Marcus
    Pages 130-157

  7. The distribution of ideals in a number ring

    • Daniel A. Marcus
    Pages 158-181

  8. The Dedekind zeta function and the class number formula

    • Daniel A. Marcus
    Pages 182-222

  9. The distribution of primes and an introduction to class field theory

    • Daniel A. Marcus
    Pages 223-250

  10. Back Matter

    Pages 251-279
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Keywords

About this book

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.

Authors and Affiliations

  • Department of Mathematics, California State Polytechnic University, Pomona, USA

    Daniel A. Marcus

Bibliographic Information

  • Book Title: Number Fields

  • Authors: Daniel A. Marcus

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4684-9356-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1977

  • eBook ISBN: 978-1-4684-9356-6Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: 292

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Number Theory, Algebra

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