# Does any fractional ideal of $R$ always contain a non-zero element of $R$?

Let $$R$$ be an integral domain. Let $$A$$ be a non-zero fractional ideal of $$R.$$ Then can we say that $$A$$ always contains a non-zero element of $$R$$?

Fractional ideals are nonzero by definition, so $$A$$ contains an element $$r/s$$ with $$r$$, $$s$$ nonzero elements of $$R$$. Then $$r=(r/s)s\in A$$.