| A Course in Algebraic Number Theory Contributor(s): Ash, Robert B. (Author) |
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ISBN: 0486477541 ISBN-13: 9780486477541 Publisher: Dover Publications OUR PRICE: $9.86 Product Type: Paperback Published: June 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | Algebra - General |
| Dewey: 512.74 |
| LCCN: 2010283195 |
| Series: Dover Books on Mathematics |
| Physical Information: 0.5" H x 5.9" W x 8.9" (0.35 lbs) 128 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |