A Course in Algebraic Number Theory
A Course in Algebraic Number Theory by Robert B. Ash is a graduate-level text published by Courier Corporation in January 2010. This edition spans 112 pages and is presented in English. The book provides comprehensive coverage for a one-semester course in algebraic number theory, focusing on the general theory of factorization of ideals in Dedekind domains and the number field case.
Readers will find detailed calculations that illustrate the application of Kummer’s theorem on lifting prime ideals in extension fields. The text includes intricate proofs of the Dirichlet unit theorem and the Minkowski bounds on element and ideal norms. Additional topics covered are the factorization of prime ideals in Galois extensions and local and global fields, along with the Artin-Whaples approximation theorem and Hensel’s lemma. The book concludes with three appendixes, making it a valuable resource for mathematics majors who have a background in graduate-level algebra and familiarity with integral extensions and localization.
Official synopsis Publisher
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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