An Introduction to Algebraic Number Theory, and the Class Number
... pAp := s / pAp , pAp 6= Ap . is the only maximal ideal in Ap . As p C A and S is multiplicatively closed, pAp C Ap . As 11 ∈ u It now suffices to prove that pAp contains all non-units in Ap . If s ∈ Ap \ pAp , then u ∈ A \ p, so us is a unit (with inverse us ) in Ap . Hence pAp contains all non-unit ...
... pAp := s / pAp , pAp 6= Ap . is the only maximal ideal in Ap . As p C A and S is multiplicatively closed, pAp C Ap . As 11 ∈ u It now suffices to prove that pAp contains all non-units in Ap . If s ∈ Ap \ pAp , then u ∈ A \ p, so us is a unit (with inverse us ) in Ap . Hence pAp contains all non-unit ...
Class Field Theory
... ramification. Made important progress in class field theory and the Kronecker Jugendtraum. H ENSEL (1861–1941). He defined the field of p-adic numbers (as the set of infinite sums ...
... ramification. Made important progress in class field theory and the Kronecker Jugendtraum. H ENSEL (1861–1941). He defined the field of p-adic numbers (as the set of infinite sums ...