Algebraic Number TheoryCourier Corporation, 1 janv. 1998 - 275 pages Careful organization and clear, detailed proofs make this book ideal either for classroom use or as a stimulating series of exercises for mathematically-minded individuals. Modern abstract techniques focus on introducing elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields. |
Table des matières
Elementary Valuation Theory | 13 |
Extension of Valuations | 41 |
Local Fields | 72 |
Ordinary Arithmetic Fields | 118 |
Global Fields | 185 |
Quadratic Fields | 233 |
Cyclotomic Fields | 255 |
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Expressions et termes fréquents
a e F a₁ algebraic number field archimedean prime basis for E/F class number closure compact composition maps Consider Corollary DE/F denote discrete prime divisor discriminant divisor of F Exercise exists exponential valuation extension E/F extension of F fact factorization field F finite extension follows Furthermore Galois extension global field homomorphism ideal of F idèle integral basis integral ideal integrally closed irreducible isomorphism lattice lemma Let F monic Moreover multiplicative nonarchimedean prime divisor nontrivial norm notation polynomial prime divisor prime element prime ideal principal ideal domain product formula Proposition quadratic field quotient field residue class residue class field restricted direct product roots of unity Suppose that F tamely ramified theory topology totally ramified trivial unique extension units unramified unramified extension valuation of F vp(a vp(B