RELATIVE GALOIS MODULE STRUCTURE OF QUADRATIC EXTENSIONS

Let N/K be a finite Galois extension of number fields with group G. Let U(N/K) = {x is-an-element-of K[G]\V(N) x subset-of V(N)} be its associated order in K[G] where K[G] is the usual group algebra. In this paper we give necessary and sufficient conditions for V(N) to be free over U(N/K) when N/K is a quadratic extension. When V(N) is free over U(N/K) we also describe a generator.