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Cyclic Galois Extensions of Commutative Rings

  • Book
  • © 1992

Overview

Authors:
  1. Cornelius Greither
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1534)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-X
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  2. Galois theory of commutative rings

    • Cornelius Greither
    Pages 1-31

  3. Cyclotomic descent

    • Cornelius Greither
    Pages 32-54

  4. Corestriction and Hilbert's Theorem 90

    • Cornelius Greither
    Pages 55-66

  5. Calculations with units

    • Cornelius Greither
    Pages 67-76

  6. Cyclic p-extensions and {ie771-}-extensions of number fields

    • Cornelius Greither
    Pages 77-96

  7. Geometric theory: cyclic extensions of finitely generated fields

    • Cornelius Greither
    Pages 97-108

  8. Cyclic Galois theory without the condition “p −1 ≥ R”

    • Cornelius Greither
    Pages 109-139

  9. Back Matter

    Pages 140-145
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Keywords

About this book

The structure theory of abelian extensions of commutative rings is a subjectwhere commutative algebra and algebraic number theory overlap. This exposition is aimed at readers with some background in either of these two fields. Emphasis is given to the notion of a normal basis, which allows one to view in a well-known conjecture in number theory (Leopoldt's conjecture) from a new angle. Methods to construct certain extensions quite explicitly are also described at length.

Bibliographic Information

  • Book Title: Cyclic Galois Extensions of Commutative Rings

  • Authors: Cornelius Greither

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0089165

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1992

  • Softcover ISBN: 978-3-540-56350-1Published: 14 December 1992

  • eBook ISBN: 978-3-540-47539-2Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 146

  • Topics: Number Theory, Algebra

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