Introductory Algebraic Number Theory

by Saban Alaca, Kenneth S. Williams

Overview

Suitable for senior undergraduates and beginning graduate students in mathematics, this book is an introduction to algebraic number theory at an elementary level. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested readings and to the biographies of mathematicians who have contributed to the development of algebraic number theory are provided at the end of each chapter. Other features include over 320 exercises, an extensive index, and helpful location guides to theorems in the text.

Product Details

ISBN-13:	9780521832502
Publisher:	Cambridge University Press
Publication date:	11/17/2003
Pages:	448
Product dimensions:	6.69(w) x 9.61(h) x 0.98(d)

Table of Contents

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.

Editorial Reviews

'The overall presentation makes the book suitable for a course for advanced undergraduate students.' Zentralblatt MATH

'Learning algebraic number theory is about the least abstract way to learn about important aspects of commutative ring theory, as well as being beautiful in its own right too. This text is ideally suited to the learner of both of these, with clear writing, a plentiful supply of examples and exercises, and a good range of 'suggested reading'. … I look forward to reading and learning from this book in greater detail. The features which make it attractive are worth listing: the intrinsic fascination of the results; the balance between clearn theory and dirty calculation (the latter essential for developing familiarity with the local terrain, the former for appreciating an arial view of the whole route); the balance between calculation dependent upon the depth of theory and those details dependent on simple algebraic and trigonometric identities and results from elementary number theory; a very full quota of exercises and further reading.' The Mathematical Gazette

'This is a very good textbook on algebraic number theory for beginners. … Its most appealing feature is the very large number of examples it contains. Their abundance provides a lot of hands-on experience and has the power to transform the reader's understanding of basic notions into active knowledge.' Monatshefte für Mathematik

'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

From the Publisher