The Decomposition of Primes in Torsion Point Fields (Paperback, 2001 ed.)

It is an historical goal of algebraic number theory to relate all algebraic extensionsofanumber?eldinauniquewaytostructuresthatareexclusively described in terms of the base ?eld. Suitable structures are the prime ideals of the ring of integers of the considered number ?eld. By examining the behaviouroftheprimeidealswhenembeddedintheextension?eld, su?cient information should be collected to distinguish the given extension from all other possible extension ?elds. The ring of integers O of an algebraic number ?eld k is a Dedekind ring. k Any non-zero ideal in O possesses therefore a decomposition into a product k of prime ideals in O which is unique up to permutations of the factors. This k decomposition generalizes the prime factor decomposition of numbers in Z Z. In order to keep the uniqueness of the factors, view has to be changed from elements of O to ideals of O . k k Given an extension K/k of algebraic number ?elds and a prime ideal p of O, the decomposition law of K/k describes the product decomposition of k the ideal generated by p in O and names its characteristic quantities, i. e. K the number of di?erent prime ideal factors, their respective inertial degrees, and their respective rami?cation indices. Whenlookingatdecompositionlaws, weshouldinitiallyrestrictourselves to Galois extensions. This special case already o?ers quite a few di?culties

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Lecture Notes in Mathematics, 1761
Release date:	May 2001
First published:	2001
Authors:	Clemens Adelmann
Dimensions:	235 x 155 x 8mm (L x W x T)
Format:	Paperback
Pages:	148
Edition:	2001 ed.
ISBN-13:	978-3-540-42035-4
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Number theory > General
LSN:	3-540-42035-5
Barcode:	9783540420354

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