Articoli correlati a Algebraic Theory Of Numbers

Algebraic Theory Of Numbers - Brossura

Samuel, Pierre

 
9780486466668: Algebraic Theory Of Numbers
Brossura
ISBN 10: 0486466663 ISBN 13: 9780486466668
Casa editrice: Dover Pubns, 2008

Sinossi

Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics — algebraic geometry, in particular.
This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Galois theory, Noetherian rings and modules, and rings of fractions. It covers the basics, starting with the divisibility theory in principal ideal domains and ending with the unit theorem, finiteness of the class number, and the more elementary theorems of Hilbert ramification theory. Numerous examples, applications, and exercises appear throughout the text.

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

Contenuti

Translator's Introduction Introduction Notations, Definitions, and Prerequisites 1. Principal ideal rings 2. Elements integral over a ring; elements algebraic over a field Appendix: The field of complex numbers is algebraically closed 3. Noetherian rings and Dedekind rings 4. Ideal classes and the unit theorem Appendix: The calculation of a volume 5. The splitting of prime ideals in an extension field 6. Galois extensions of number fields A supplement, without proofs Exercises Bibliography Index

Product Description

Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition.

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

Editore
Dover Pubns
Data di pubblicazione
2008
Lingua
Inglese
ISBN 10 
0486466663
ISBN 13 
9780486466668
Rilegatura
Copertina flessibile
Numero di pagine
109
Contatto del produttore
non disponibile
Persona responsabile
Soc. Agr. La Raia Ss
http://www.la-raia.it

Strada Monterotondo, 79
Novi Ligure
15067
Italia