Synopses & Reviews
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
Includes bibliographical references (p. ) and indexes.
Table of Contents
Contents: A special case of Fermat's conjecture.- Number fields and number rings.- Prime decomposition in number rings.- Galois theory applied to prime decomposition.- The ideal class group and the unit group.- The distribution of ideals in a number ring.- The Dedekind zeta function and the class number formula.- The distribution of primes and an introduction to class field theory.