A Course In Algebraic Number Theory
Author :
Robert B. Ash,
Department of Mathematics,
University of Illinois
Publication Date : 2003
Terms and Conditions:
| Robert B. Ash wrote: |
| (C) Copyright 2003, by Robert B. Ash. Paper or electronic copies for noncommercial use may be made freely without explicit permission of the author. All other rights are reserved. |
This is a text for a basic course in
algebraic number theory, written in accordance with the following objectives:
1. Provide reasonable coverage for a one-semester course.
2. Assume as prerequisite a standard graduate course in algebra, but cover integral extensions and localization before beginning algebraic number theory. For general algebraic background, see author's online text "
Abstract Algebra: The Basic Graduate Year". The abstract algebra material is referred to in this text as TBGY.
3. Cover the general theory of factorization of ideals in
Dedekind domains, as well as the number field case.
4. Do some detailed calculations illustrating the use of
Kummer's theorem on lifting of prime ideals in extension fields.
5. Give enough details so that the reader can navigate through the intricate proofs of the
Dirichlet unit theorem and the
Minkowski bounds on element and ideal norms.
6. Cover the factorization of prime ideals in
Galois extensions.
7. Cover local as well as global fields, including the
Artin-Whaples approximation theorem and
Hensel's lemma.
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