I hope to get a hint for this one.
Let $R$ be an integral domain for which $IJ = I∩J$ for all ideals of $R$. Then $R$ is a field.
2026-04-07 04:47:55.1775537275
R is a commutative ring with unity, let R be an integral domain for which IJ = I∩J for all ideals of R then R is a field
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Hint:
$IJ=I\cap J$ means that every prime ideal in $R$ is maximal. Then use $R[x]/(x)\cong R$.