Cyclic Galois Extensions of Commutative Rings

ISBN-13: 9783540563501 / Angielski / Miękka / 1992 / 146 str.

Cornelius Greither

Opis

The structure theory of abelian extensions of commutativerings is a subjectwhere commutative algebra and algebraicnumber theory overlap. This exposition is aimed at readerswith some background in either of these two fields. Emphasisis given to the notion of a normal basis, which allows oneto view in a well-known conjecture in number theory(Leopoldt's conjecture) from a new angle. Methods toconstruct certain extensions quite explicitly are alsodescribed at length.

Spis treści

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”.