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 $R$?
Please help me in this regard. Thank you very much.
Fractional ideals are nonzero by definition, so $A$ contains an element $r/s$ with $r$, $s$ nonzero elements of $R$. Then $r=(r/s)s\in A$.