Full Description
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.
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".
