Cyclic Galois Extensions of Commutative Rings

Cornelius Greither (Autor)

Buch | Softcover

X, 146 Seiten

1992 | 1992
Springer Berlin (Verlag)
978-3-540-56350-1 (ISBN)

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The structure theory of abelian extensions of commutativerings is a subjectwhere commutative algebra and algebraicnumber theory overlap. This exposition is aimed at readerswith some background in either of these two fields. Emphasisis given to the notion of a normal basis, which allows oneto view in a well-known conjecture in number theory(Leopoldt's conjecture) from a new angle. Methods toconstruct certain extensions quite explicitly are alsodescribed 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 "p ?1 ? R".

Erscheint lt. Verlag	14.12.1992
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	X, 146 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	246 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Algebra • algebraic number theory • Commutative algebra • Commutative Ring • Galois Theory • Number Theory
ISBN-10	3-540-56350-4 / 3540563504
ISBN-13	978-3-540-56350-1 / 9783540563501
Zustand	Neuware