Scaling of Fractional ideals

Question

For fractional ideals of a Dedekind Domain, are each of the elements that generate the ideal (ie. form the basis of the lattice associated with the ideal) always scaled by the same amount? That is to say, scaled by the same element from the field of fractions?

Answer 1

I'm not sure if I understand the question, but a fractional ideal is a fraction times an actual ideal, by the definition, i.e. for a fractional ideal $I$ over a ring $R$ we have some $r\in R$ such that $rI\unlhd R$.