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Arithmetic in Relative Extensions
Geometry of Numbers
6 other sections not shown
A-module Abelian extension absolute value algebraic integer Artin symbol basis called choose class number commutative ring conjugates Corollary coset curve cyclic extension cyclic group cyclotomic field Dedekind domain Dedekind zeta function defined Definition degree denote discriminant distinct primes dividing equation Exercise extension K/k extension of number finite field fixed field fractional ideal full lattice fundamental domain fundamental parallelepiped Gal(K/k Galois extension Galois group given Hence ideal class ideal of Ok implies integral domain integral ideal isomorphic matrix monic polynomial non-zero element non-zero ideal norm number field powers of distinct prime divisor prime ideal prime to ramify primitive m-th root principal ideal Proof Let Proposition prove Q-isomorphisms Q(Cm quadratic field quotient Recall Riemann Hypothesis ring of integers roots of unity Rri+r2 square-free integer subfield subgroup subring subset Theorem totally ramified unique factorization unramified vector space zero