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A Course in Algebraic Number Theory

by Robert B. Ash

2021-01-01 02:12:22

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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 ... Read more
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. Less

Book Details

File size9 X 6 X 0.68 in
Print pages128
PublisherDover Publications
Publication date June 17, 2010
LanguageEnglish
ISBN9780486477541
autor-image
Robert B. Ash
Author
A Professor Emeritus of Mathematics at the University of Illinois, Robert Ash is the author of three other Dover books: Basic Abstract Algebra, Basic Probability Theory, and Complex Variables and Info...

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