Galoismodulstruktur und elliptische funktionen

Abstract

Let K be a quadratic imaginary number field, ▪ an integral ideal in K and K( ▪) the ray class field modulo ▪ over K. For certain extensions K( ▪)/ K( ▪ ∗), ▪ ∗| ▪, it is shown that the ring of integers in K( ▪) is a free rank one module over the associated order (1.2) of K( ▪)/ K( ▪ ∗) in the group ring of Gal( K( ▪)/ K( ▪ ∗)) on K( ▪ ∗). The associated order and generating elements are both constructed by elliptic functions.