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＜電子ブック＞
Class Field Theory / by Nancy Childress
(Universitext. ISSN:21916675)

版	1st ed. 2009.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	X, 226 p : online resource
著者標目	*Childress, Nancy author SpringerLink (Online service)
件　名	LCSH:Algebraic fields LCSH:Polynomials LCSH:Number theory FREE:Field Theory and Polynomials FREE:Number Theory
一般注記	A Brief Review -- Dirichlet#x2019;s Theorem on Primes in Arithmetic Progressions -- Ray Class Groups -- The Id#x00E8;lic Theory -- Artin Reciprocity -- The Existence Theorem, Consequences and Applications -- Local Class Field Theory Class field theory, the study of abelian extensions of algebraic number fields, is one of the largest branches of algebraic number theory. It brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. Some of its consequences (e.g., the Chebotarev density theorem) apply even to nonabelian extensions.   This book is an accessible introduction to class field theory. It takes a traditional approach in that it presents the global material first, using some of the original techniques of proof, but in a fashion that is cleaner and more streamlined than most other books on this topic.   It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included exercises throughout the text.   Professor Nancy Childress is a member of the Mathematics Faculty at Arizona State University HTTP:URL=https://doi.org/10.1007/978-0-387-72490-4

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