A Course in Algebraic Number Theory (Dover Books on Mathematics)

Robert B. Ash

ISBN 10: 0486477541 / ISBN 13: 9780486477541

Editore: Dover Publications, 2010

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Codice articolo STK-07-G-06-9780486477541

Dati bibliografici

• Titolo: A Course in Algebraic Number Theory (Dover Books on Mathematics)
• Editore: Dover Publications
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 0486477541
• ISBN 13: 9780486477541
• Rilegatura: Brossura
• Condizione: New
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Descrizione articolo

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