Cyclic Galois Extensions of Commutative Rings / Edition 1

by Cornelius Greither

Overview

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.

Product Details

ISBN-13:	9783540563501
Publisher:	Springer Berlin Heidelberg
Publication date:	01/26/1993
Series:	Lecture Notes in Mathematics , #1534
Edition description:	1992
Pages:	146
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

Galois theory of commutative rings.- Cyclotomic descent.- Corestriction and Hilbert's Theorem 90.- Calculations with units.- Cyclic p-extensions and {ie771-}-extensions of number fields.- Geometric theory: cyclic extensions of finitely generated fields.- Cyclic Galois theory without the condition “p—1— R”.