Introductory algebraic number theory / Şaban Alaca, Kenneth S. Williams.

Format:

Book

Author/Creator:

Alaca, Şaban, 1964- author.

Williams, Kenneth S., author.

Language:

English

Subjects (All):

Algebraic number theory--Textbooks.

Algebraic number theory.

Physical Description:

1 online resource (xvii, 428 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2004.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 423-424) and index.

ISBN:

1-107-14885-5

0-511-79126-7

0-511-16609-5

0-511-16414-9

0-511-56680-8

0-511-16494-7

OCLC:

437165582