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  • © 1992

Cyclic Galois Extensions of Commutative Rings

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
  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. Back Matter

    Pages 140-145

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.

Keywords

  • Galois theory
  • algebra
  • algebraic number theory
  • commutative algebra
  • commutative ring
  • number theory

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

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions