Cyclic Galois Extensions of Commutative Rings / Cornelius Greither

Date :

Type : Livre / Book

Langue / Language : anglais / English

ISBN : 978-3-540-47539-2

Théorie des nombres

Extensions de corps (mathématiques)

Galois, Théorie de

Algèbre

Anneaux commutatifs

Classification Dewey : 510

Collection : Lecture notes in mathematics / Heidelberg : Springer , 2001-

Relation : Cyclic Galois extensions of commutative rings / Cornelius Greither / Berlin : Springer

Résumé / Abstract : 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.