Let $R$ be a commutative ring with $1$ and $e$ be an idempotent element of $R$ with the property that if $e=x+y$ (where $x, y\in R$), then there exists $r\in R$ such that either $e=rx$ or $e=ry$. Can we deduced that for such an idempotent, the ideal $\langle e\rangle$ is a minimal ideal of $R$?
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Martin Sleziak
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Special idempotents in a commutative ring
user140640
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