Articoli correlati a A Course in Algebraic Number Theory

A Course in Algebraic Number Theory - Brossura

Libro 19 di 303: Dover Books on Mathematics

Ash, Robert B.

 
9780486477541: A Course in Algebraic Number Theory
Brossura
ISBN 10: 0486477541 ISBN 13: 9780486477541
Casa editrice: Dover Pubns, 2010

Sinossi

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

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

Product Description

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.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Dover Pubns
Data di pubblicazione
2010
Lingua
Inglese
ISBN 10 
0486477541
ISBN 13 
9780486477541
Rilegatura
Copertina flessibile
Numero di pagine
112
Contatto del produttore
non disponibile
Persona responsabile
Soc. Agr. La Raia Ss
http://www.la-raia.it

Strada Monterotondo, 79
Novi Ligure
15067
Italia