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Catalogue Information
Field name	Details
Dewey Class	512.74
Title	Class Field Theory ([Ebook]) / by Nancy Childress.
Author	Childress, Nancy
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 2009.
Physical Details	X, 226 pages : online resource.
Series	Universitext
ISBN	9780387724904
Summary Note	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.:
Contents note	Preface -- A Brief Review -- Dirichlet's Theorem on Primes in Arithmetic Progressions -- Ray Class Groups -- The Idelic Theory -- Artin Reciprocity -- The Existence Theorem, Consequences and Applications -- Local Class Field Theory -- Bibliography -- Index.
System details note	Online access is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-387-72490-4
Links to Related Works	Subject References: Field Theory and Polynomials . Field theory (Physics) . Mathematics . Number Theory . Authors: Childress, Nancy . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 512.74 . 512.74 (DDC 22) .

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Class Field Theory

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