Galois Structure of Rings of Integers and Elliptic Curves without Complex Multiplication Original Research Article

In this paper we state the problem of Galois module structure of rings of integers of extensions attached to the elliptic curves without complex multiplication and admitting a rational point of finite order. Our main aim is to give the first results related to this problem. These results are an analogous to the results of others, concerning ray class fields in the complex multiplication case.