This text covers the basics of algebraic number theory, including divisibility theory in principal ideal domains, the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition.
This text covers the basics of algebraic number theory, including divisibility theory in principal ideal domains, the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition.
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
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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