Algebraic Number Theory
Courier 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.
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Elementary Valuation Theory
Extension of Valuations
Ordinary Arithmetic Fields
Autres éditions - Tout afficher
According additive algebraic number field apply archimedean assertion belonging called choose class number clear Clearly closed compact complete Consequently Consider contains Corollary corresponding course defined definition denote determined discrete discriminant distinct domain easy element equation equivalent example Exercise exists fact factorization field field F finite extension fixed follows formula function fundamental Furthermore give given global Hence immediate implies integral basis introduction irreducible isomorphism known lemma MATHEMATICS means Moreover multiplicative nonarchimedean norm normalized observe particular polynomial prime divisor prime ideal principal problems Proof properties Proposition prove quadratic quantum mechanics ramified relation remains residue class respect result ring roots of unity separable situation solution Suppose theorem theory topology trivial unique units unramified valuation vp(a write