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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.

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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 $r=(r/s)s\in A$.

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  • $\begingroup$ Oh! I see. Thanks @Lord Shark The Unknown for your kind help. $\endgroup$ – math maniac. Mar 4 at 6:52

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