Table of Contents

Translator's Introduction Introduction Notations, Definitions, and Prerequisites 1. Principal ideal rings 2. Elements integral over a ring; elements algebraic over a field Appendix: The field of complex numbers is algebraically closed 3. Noetherian rings and Dedekind rings 4. Ideal classes and the unit theorem Appendix: The calculation of a volume 5. The splitting of prime ideals in an extension field 6. Galois extensions of number fields A supplement, without proofs Exercises Bibliography Index