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.
2026-03-25 09:39:59.1774431599
Does any fractional ideal of $R$ always contain a non-zero element of $R$?
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Fractional ideals are nonzero by definition, so $A$ contains an element $r/s$ with $r$, $s$ nonzero elements of $R$. Then $r=(r/s)s\in A$.