Cyclic Galois Extensions of Commutative Rings [electronic resource] / by Cornelius Greither.

By:

Greither, Cornelius [author.]

Contributor(s):

SpringerLink (Online service)

Material type: Text

TextSeries: Lecture Notes in Mathematics ; 1534Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992Description: X, 146 p. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783540475392

Subject(s):

Additional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification:

512.7 23

LOC classification:

QA241-247.5

Online resources:

Click here to access online

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”.

In: Springer eBooksSummary: 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.

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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.

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