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Class Field Theory Nancy Childress

Class Field Theory By Nancy Childress

Class Field Theory by Nancy Childress


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Summary

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.

Class Field Theory Summary

Class Field Theory by Nancy Childress

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.

Class Field Theory 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 ... . (Jurgen 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 fur Mathematik, Vol. 164 (3), November, 2011)

Table of Contents

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.

Additional information

NLS9780387724898
9780387724898
0387724893
Class Field Theory by Nancy Childress
New
Paperback
Springer-Verlag New York Inc.
2008-11-24
226
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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