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A Classical Invitation to Algebraic Numbers and Class Fields

  • Textbook
  • © 1978

Overview

Authors:
  1. Harvey Cohn

    1. City College, City University of New York, New York, USA

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Part of the book series: Universitext (UTX)

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Table of contents (19 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Preliminaries

    1. Front Matter

      Pages N1-N1
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    2. Introductory Remarks on Quadratic Forms

      • Harvey Cohn
      Pages 1-5

    3. Algebraic Background

      • Harvey Cohn
      Pages 6-16

    4. Quadratic Euclidean Rings

      • Harvey Cohn
      Pages 17-23

    5. Congruence Classes

      • Harvey Cohn
      Pages 24-33

    6. Polynomial Rings

      • Harvey Cohn
      Pages 34-41

    7. Dedekind Domains

      • Harvey Cohn
      Pages 42-52

    8. Extensions of Dedekind Domains

      • Harvey Cohn
      Pages 53-65

    9. Rational and Elliptic Functions

      • Harvey Cohn
      Pages 66-71

  3. Ideal Structure in Number Fields

    1. Front Matter

      Pages N2-N2
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    2. Basis and Discriminant

      • Harvey Cohn
      Pages 72-85

    3. Prime Factorization

      • Harvey Cohn
      Pages 86-101

    4. Units

      • Harvey Cohn
      Pages 102-113

    5. Geometry of Numbers

      • Harvey Cohn
      Pages 114-124

    6. Finite Determination of Class Number

      • Harvey Cohn
      Pages 125-136

  4. Introduction to Class Field Theory

    1. Front Matter

      Pages N3-N3
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    2. Quadratic Forms, Rings and Genera

      • Harvey Cohn
      Pages 137-162

    3. Ray Class Structure and Fields, Hilbert Class Fields

      • Harvey Cohn
      Pages 163-187

    4. Hilbert Sequences

      • Harvey Cohn
      Pages 188-207
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Keywords

Authors and Affiliations

  • City College, City University of New York, New York, USA

    Harvey Cohn

Bibliographic Information

  • Book Title: A Classical Invitation to Algebraic Numbers and Class Fields

  • Authors: Harvey Cohn

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4612-9950-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1978

  • Softcover ISBN: 978-0-387-90345-3Published: 21 September 1978

  • eBook ISBN: 978-1-4612-9950-9Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: 328

  • Topics: Number Theory

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