Class Field Theory

Nancy Childress

ISBN 10: 0387724893 / ISBN 13: 9780387724898

Published by Springer, 2009

About this Item

Spine is slightly cracked. Cover is lightly worn. Inside is clean and unmarked.

Seller Inventory # 1139619

Bibliographic Details

• Title: Class Field Theory
• Publisher: Springer
• Publication Date: 2009
• Language: English
• ISBN 10: 0387724893
• ISBN 13: 9780387724898
• Binding: Soft cover
• Condition: Good
• Dust Jacket Condition: No jacket
• Seller catalogs:
  • Mathematics

About this title

Synopsis

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 attempts to present the material using the original techniques of proof (global to local), but in a fashion which 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.

From the Back Cover

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.