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 Title A Course in Algebraic Number Theory
 Author(s) Robert B. Ash
 Publisher: Dover Publications (November 1, 1990)
 Hardcover/Paperback 600 pages
 eBook PDF files
 Language: English
 ISBN10: 0486477541
 ISBN13: 9780486477541
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Book Description
This graduatelevel text provides coverage for a onesemester 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 ArtinWhaples approximation theorem and Hensel's lemma. The text concludes with three helpful appendixes. Geared toward mathematics majors, this course requires a background in graduatelevel algebra and a familiarity with integral extensions and localization.
About the Authors Robert B. Ash (19352015) is Professor Emeritus of Mathematics in the Department of Mathematics at the University of Illinois.