Algebraic Number Theory [Paperback]

A graduate text providing a brisk, thorough treatment of the foundations of algebraic number theory.The systematic development of techniques for the explicit calculation of the basic invariants such as rings of integers, class groups, and units, is emphasized throughout this introduction to the foundations of algebraic number theory.The systematic development of techniques for the explicit calculation of the basic invariants such as rings of integers, class groups, and units, is emphasized throughout this introduction to the foundations of algebraic number theory.This book provides a brisk, thorough treatment of the foundations of algebraic number theory on which it builds to introduce more advanced topics. Throughout, the authors emphasize the systematic development of techniques for the explicit calculation of the basic invariants such as rings of integers, class groups, and units, combining at each stage theory with explicit computations.Notation; Introduction; 1. Algebraic foundations; 2. Dedekind domains; 3. Extensions; 4. Classgroups and units; 5. Fields of low degree; 6. Cyclotomic fields; 7. Diophantine equations; 8. L-functions; Appendices; Exercises; Glossary of theorems; Index. ...an excellent contribution to the long list of books presenting the main results of algebraic number theory. It is useful for anyone who is learning or teaching this branch of mathematics. J. Browkin, Mathematical Reviews