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
Summary
An introduction to algebraic number theory for senior undergraduates and beginning graduate students in mathematics. It includes numerous examples, and references to further reading and to biographies of mathematicians who have contributed to the development of the subject. Includes over 320 exercises, and an extensive index
Bibliography
Includes bibliographical references (pages 423-424) and index
