Let $K$ be a number field and let $\mathcal O_K$ be its ring of integers. Let $I$ be a non-zero ideal in $\mathcal O_K$.
If $I$ is free as a $\mathcal O_K$-module then is it a principal ideal?
I know that any (fractional) $\mathcal O_K$-ideal is generated by at most two elements since $\mathcal O_K$ is Dedekind but is there an easy way to show the above?
Many thanks.