Items related to Algebraic Number Fields (Graduate Studies in Mathematics,...

Algebraic Number Fields (Graduate Studies in Mathematics, 7) - Hardcover

Book 57 of 190: Graduate Studies in Mathematics

Gerald J. Janusz

  • 4.43 out of 5 stars
    7 ratings by Goodreads
 
9780821804292: Algebraic Number Fields (Graduate Studies in Mathematics, 7)
Hardcover
ISBN 10: 0821804294 ISBN 13: 9780821804292
Publisher: American Mathematical Society, 2005

Synopsis

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.

"synopsis" may belong to another edition of this title.

Review

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

"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

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2005
Language
English
ISBN 10 
0821804294
ISBN 13 
9780821804292
Binding
Hardcover
Edition number
2
Number of pages
276
Rating
  • 4.43 out of 5 stars
    7 ratings by Goodreads