TY  - BOOK
AU  - Januz, Gerald J. 
TI  - Algebraic number fields
SN  - 9780821852194
AV  - QA3 
PY  - 1996///]
CY  - Rhode Island
PB  - AMS
KW  - Mathematics
N1  - Chapter I. Subrings of fields
Chapter II. Complete fields
Chapter III. Decomposition groups and the Artin map
Chapter IV. Analytic methods and Ray classes
Chapter V. Class field theory
Chapter VI. Quadratic fields

N2  - 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
ER  -