Let $R$ be a Dedekind domain with fractional ideal $M$. I am trying to prove:
If $M$ is free, then the ideal $I$ such that $M=d^{-1}I$, where $d \in R$, is principal.
Since $R$ is a Dedekind domain we can conclude $M$ is generated by at most two elements. I've been trying for a while, but I don't know how to conclude $I$ is principal. Any ideas?