Paperback. This text for a graduate-level course covers the general theory of factorization of ideals in Dedekind domains as well as the number field case. It illustrates the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780486477541

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Titolo: A Course in Algebraic Number Theory (Paperback)
Editore: Dover Publications, New York
Data di pubblicazione: 2010
Lingua: Inglese
ISBN 10: 0486477541
ISBN 13: 9780486477541
Rilegatura: Paperback
Condizione: new

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Riassunto

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.

Contenuti

1. 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

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