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Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger
Contributor(s): Samuel, Pierre (Author), Silberger, Allan J. (Translator)

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 ISBN: 0486466663     ISBN-13: 9780486466668
Publisher: Dover Publications
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Binding Type: Paperback - See All Available Formats & Editions
Published: May 2008
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Annotation: 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.

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Additional Information
BISAC Categories:
- Mathematics | Number Theory
- Mathematics | Algebra - General
Dewey: 512.74
LCCN: 2007049457
Series: Dover Books on Mathematics
Physical Information: 0.23" H x 6.19" W x 9.16" L (0.35 lbs) 112 pages
Features: Bibliography, Index, Price on Product, Table of Contents
 
Descriptions, Reviews, Etc.
Publisher Description:
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.
 
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