Introductory Algebraic Number Theory

This book provides an introduction to algebraic number theory suitable for senior undergraduates and beginning graduate students in mathematics.

Saban Alaca (Author), Kenneth S. Williams (Author)

9780521832502, Cambridge University Press

Hardback, published 17 November 2003

448 pages, 16 tables 320 exercises
24.4 x 17 x 2.5 cm, 0.91 kg

'This book provides a nice introduction to classical parts of algebraic number theory.… The text is written in a lively style and can be read without any prerequisites. Therefore the book is very suitable for graduate students starting mathematics courses or mathematicians interested in introductory reading in algebraic number theory. The book presents a welcome addition to the existing literature.' EMS Newsletter

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.

Introduction
1. Integral domains
2. Euclidean domains
3. Noetherian domains
4. Elements integral over a domain
5. Algebraic extensions of a field
6. Algebraic number fields
7. Integral bases
8. Dedekind domains
9. Norms of ideals
10. Decomposing primes in a number field
11. Units in real quadratic fields
12. The ideal class group
13. Dirichlet's unit theorem
14. Applications to diophantine equations.

Subject Areas: Number theory [PBH]