Class Field Theory

Paperback | November 24, 2008

byNancy Childress

not yet rated|write a review
Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides 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, 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 lots of challenging exercises throughout the text.

Pricing and Purchase Info

$77.95

In stock online
Ships free on orders over $25

From the Publisher

Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides 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, but in a fashi...

From the Jacket

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 t...

Format:PaperbackDimensions:236 pages, 0.35 × 0.25 × 0.03 inPublished:November 24, 2008Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387724893

ISBN - 13:9780387724898

Look for similar items by category:

Customer Reviews of Class Field Theory

Reviews

Extra Content

Table of Contents

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.

Editorial Reviews

From the reviews:"This book has grown out of lectures on the subject by the author. . it must have been fun for both the author presenting these courses on class field theory and the students taking them and eager to learn the subject. . list of contents may give a good impression of how class field theory is developed in this book. . each chapter is commenced by a short introduction describing what is going on next. I enjoyed seeing explicit examples and nice applications . ." (Jürgen Ritter, Mathematical Reviews, Issue 2009 i)"Class field theory studies abelian extensions of number fields and their completions. . The clarity of the exposition and the many exercises ranging from routine to quite challenging problems make the book perfect for a first introduction to class field theory." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1165, 2009)"In a fast ride, running half the length of many competing volumes, Childress (Arizona State) employs a balanced mix of standard tools for a remarkably honed introduction . . Good to read alongside fleshier accounts; probably more accessible . . Summing Up: Recommended. Upper-division undergraduates through researchers/faculty." (D. V. Feldman, Choice, Vol. 47 (3), November, 2009)"This is a first introduction to class field theory. . The author succeeds in making the material accessible by proceeding at a moderate pace. This relatively slim book is a good choice for anyone who wants to get an idea of what class field theory is about before tackling a more comprehensive textbook or monograph." (Ch. Baxa, Monatshefte für Mathematik, Vol. 164 (3), November, 2011)