Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger (Dover Books on Mathematics) (Paperback)

Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger (Dover Books on Mathematics) Cover Image
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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.
Product Details
ISBN: 9780486466668
ISBN-10: 0486466663
Publisher: Dover Publications
Publication Date: May 19th, 2008
Pages: 109
Language: English
Series: Dover Books on Mathematics