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AuthorGreither, Cornelius. author
TitleCyclic Galois Extensions of Commutative Rings [electronic resource] / by Cornelius Greither
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1992
Connect tohttp://dx.doi.org/10.1007/BFb0089165
Descript X, 146 p. online resource

SUMMARY

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


CONTENT

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}


Mathematics Algebra Number theory Mathematics Number Theory Algebra



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