Cyclic Galois Extensions of Commutative Rings

Cornelius Greither (auth.)9780387563503, 0-387-56350-4, 3540563504

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.

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Table of contents :
Galois theory of commutative rings….Pages 1-31
Cyclotomic descent….Pages 32-54
Corestriction and Hilbert’s Theorem 90….Pages 55-66
Calculations with units….Pages 67-76
Cyclic p -extensions and {ie771-}-extensions of number fields….Pages 77-96
Geometric theory: cyclic extensions of finitely generated fields….Pages 97-108
Cyclic Galois theory without the condition “ p −1 ≥ R ”….Pages 109-139