Algebraic Number Fields by Gerald J Janusz

Algebraic Number Fields by Gerald J Janusz

The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in number fields, such as the arithmetic of fields, Dedekind domains, and valuations. The next two chapters discuss class field theory for number fields. The concluding chapter serves as an illustration of the concepts introduced in previous chapters. In particular, some interesting calculations with quadratic fields show the use of the norm residue symbol. For the second edition the author added some new material, expanded many proofs, and corrected errors found in the first edition. The main objective, however, remains the same as it was for the first edition: to give an exposition of the introductory material and the main theorems about class fields of algebraic number fields that would require as little background preparation as possible. Janusz's book can be an excellent textbook for a year-long course in algebraic number theory; the first three chapters would be suitable for a one-semester course. It is also very suitable for independent study.

Gives a highly readable introduction into class field theory.. clearly written and may be recommended to everybody interested in the subject."" — Zentralblatt MATH

""Provides a quick and self-contained introduction to the subject using only limited mathematical tools, hence it is accessible to a broader audience than most of the other texts on this topic."" —Mathematical Reviews

Gerald J. Janusz, University of Illinois, Urbana, IL

SKU	Unavailable
ISBN 13	9781470484750
ISBN 10	1470484757
Title	Algebraic Number Fields
Author	Gerald J Janusz
Series	Graduate Studies In Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	American Mathematical Society
Year published	1996-01-30
Number of pages	276
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.