Introductory algebraic number theory

Saban Alaca, Kenneth S. Williams

446 pages, parution le 15/01/2004

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Résumé

Algebraic number theory is a subject which came into being through the attempts of mathematicians to try to prove Fermat's last theorem and which now has a wealth of applications to diophantine equations, cryptography, factoring, primality testing and public-key cryptosystems. This book provides an introduction to the subject suitable for senior undergraduates and beginning graduate students in mathematics. The material is presented in a straightforward, clear and elementary fashion, and the approach is hands on, with an explicit computational flavour. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested reading and to the biographies of mathematicians who have contributed to the development of algebraic number theory are given at the end of each chapter. There are over 320 exercises, an extensive index, and helpful location guides to theorems and lemmas in the text.

Sommaire

Introduction
Integral domains
Euclidean domains
Noetherian domains
Elements integral over a domain
Algebraic extensions of a field
Algebraic number fields
Integral bases
Dedekind domains
Norms of ideals
Decomposing primes in a number field
Units in real quadratic fields
The ideal class group
Dirichlet's unit theorem
Applications to diophantine equations.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Saban Alaca, Kenneth S. Williams
Parution	15/01/2004
Nb. de pages	446
Format	17,5 x 25,2
Couverture	Broché
Poids	770g
Intérieur	Noir et Blanc
EAN13	9780521540117
ISBN13	978-0-521-54011-7