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QUADRATIC EUCLIDEAN RINGS
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abelian extension algebraic number field algebraic number theory Artin automorphisms base field basis called Chapter class field theory class group class number computation conductor congruence conjugates consider Corollary corresponding cosets cyclic Dedekind ring define Definition degree denote determined Dirichlet elements equation equivalence euclidean Exercise exists extension field finite number follows fundamental unit genus group H Hasse Hence Hilbert class field Hilbert sequence ideal class Illustration imbedding infinite integral domain invariant irreducible isomorphic K/ko L-function L-series Lemma Math matrix maximal module modulo monic norm normal Pell's equation polynomial prime factor prime ideals principal ideal Proof Q(exp quadratic field quadratic forms R-module ramified primes rational relation relatively prime Remark representation represented residue classes result Riemann surface roots of unity satisfies solvable split completely subfield subgroup symbol Taussky Theorem Type unimodular unique factorization unramified vector Verify