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A Course in Algebraic Number Theory - (Dover Books on Mathematics) by Robert B Ash (Paperback)

About this item

Specifications

Number of Pages: 112

Genre: Mathematics

Sub-Genre: Number Theory

Series Title: Dover Books on Mathematics

Format: Paperback

Publisher: Dover Publications

Age Range: Adult

Author: Robert B Ash

Language: English

Street Date: June 17, 2010
TCIN: 77741106
UPC: 9780486477541
Item Number (DPCI): 247-61-7905
Origin: Made in the USA or Imported

Description



About the Book



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.



Book Synopsis



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.
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