Author	Greither, Cornelius. author
Title	Cyclic Galois Extensions of Commutative Rings [electronic resource] / by Cornelius Greither
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1992
Connect to	http://dx.doi.org/10.1007/BFb0089165
Descript	X, 146 p. online resource

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

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 โ{128}{156}p ?1 ? Rโ{128}{157}