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25 Remote Warehouse Mathematics- Number Theory

A Course in Algebraic Number Theory

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A Course in Algebraic Number Theory Cover

 

Synopses & Reviews

Publisher Comments:

This graduate-level text provides coverage for a one-semester course in algebraic number theory. It explores the general theory of factorization of ideals in Dedekind domains as well as the number field case. Detailed calculations illustrate the use of Kummer's theorem on lifting of prime ideals in extension fields.

The author provides sufficient details for students to navigate the intricate proofs of the Dirichlet unit theorem and the Minkowski bounds on element and ideal norms. Additional topics include the factorization of prime ideals in Galois extensions and local as well as global fields, including the Artin-Whaples approximation theorem and Hensel's lemma. The text concludes with three helpful appendixes. Geared toward mathematics majors, this course requires a background in graduate-level algebra and a familiarity with integral extensions and localization.

Synopsis:

Graduate-level course covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.

Synopsis:

Graduate-level course covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.

Table of Contents

1. Introduction
2. Norms, Traces and Discriminants
3. Dedekind Domains
4. Factorization of Prime Ideals in Extensions
5. The Ideal Class Group
6. The Dirichlet Unit Theorem
7. Cyclotomic Extensions
8. Factorization of Prime Ideals in Galois Extensions
9. Local Fields
Appendices
Solutions to Problems
Index

Product Details

ISBN:
9780486477541
Author:
Ash, Robert B.
Publisher:
Dover Publications
Author:
Mathematics
Subject:
Algebra - General
Subject:
Number Theory
Subject:
Algebraic number theory
Subject:
Factorization of ideals
Subject:
Dedekind domains
Subject:
Mathematics-Number Theory
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20100631
Binding:
TRADE PAPER
Language:
English
Pages:
126
Dimensions:
9 x 6 in 0.37 lb

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Related Subjects


Science and Mathematics » Mathematics » Algebra » General
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A Course in Algebraic Number Theory New Trade Paper
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Product details 126 pages Dover Publications - English 9780486477541 Reviews:
"Synopsis" by ,
Graduate-level course covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.
"Synopsis" by ,
Graduate-level course covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.
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