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A Course in Algebraic Number Theoryby Robert B. Ash
Synopses & ReviewsPublisher Comments: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. Synopsis:Graduatelevel 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. Synopsis:Graduatelevel 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. Table of Contents1. Introduction 2. Norms, Traces and Discriminants 3. Dedekind Domains 4. Factorization of Prime Ideals in Extensions 5. The Ideal Class Group 6. The Dirichlet Unit Theorem 7. Cyclotomic Extensions 8. Factorization of Prime Ideals in Galois Extensions 9. Local Fields Appendices Solutions to Problems Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
Other books you might likeRelated SubjectsScience and Mathematics » Mathematics » Algebra » General Science and Mathematics » Mathematics » General Science and Mathematics » Mathematics » Number Theory Science and Mathematics » Mathematics » Topology 

