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Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger by Pierre Samuel ISBN: 0486466663 Dover Publications Price: $10.95 click here to see this book Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition. Reprint of the Hermann, Paris, and Houghton Mifflin Company, Boston, 1970 edition. Table of Contents for Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger 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

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