01854 2200217 4500
FRBNF375180020000004
0821804294
rel.
5679
5679
19970806d m y0frey5003 b
eng
eng
Algebraic number fields
MON
Gerald J.Janusz
2nd ed.
American Mathematical Society
1996
Providence
276 p.
Graduate studies in mathematics
7
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 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.
Corps de classe
Corps algébriques
Algèbre
512.2 Arithmétique, courbes algébriques
Janusz
Gerald J.
12342
5795
ENSB
ENSB
MATHEMATIQUES
00005698
512.2 JAN
2007-06-25
0
512.2 Arithmétique, courbes algébriques