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Removed the deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)
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Martin Sleziak
Martin Sleziak
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Let $R $ be a commutative ring with 1 and $s $ a nonnilpotent element of $R $ such that for each idempotent $e $ of $R $ there exists a natural number $n_e $ such that either $s^{n_e}e=0$ or $s^{n_e}(1-e)=0$. Can we deduceddeduce that for each idempotent $e $$e$ of $R $$R$ either $s^me=0$ or $s^m(1-e)=0$ for a fix natUralnatural number $m $?

Let $R $ be a commutative ring with 1 and $s $ a nonnilpotent element of $R $ such that for each idempotent $e $ of $R $ there exists a natural number $n_e $ such that either $s^{n_e}e=0$ or $s^{n_e}(1-e)=0$. Can we deduced that for each idempotent $e $ of $R $ either $s^me=0$ or $s^m(1-e)=0$ for a fix natUral number $m $?

Let $R $ be a commutative ring with 1 and $s $ a nonnilpotent element of $R $ such that for each idempotent $e $ of $R $ there exists a natural number $n_e $ such that either $s^{n_e}e=0$ or $s^{n_e}(1-e)=0$. Can we deduce that for each idempotent $e$ of $R$ either $s^me=0$ or $s^m(1-e)=0$ for a fix natural number $m $?

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arenna
arenna
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Annihilator of idempotent elements

Let $R $ be a commutative ring with 1 and $s $ a nonnilpotent element of $R $ such that for each idempotent $e $ of $R $ there exists a natural number $n_e $ such that either $s^{n_e}e=0$ or $s^{n_e}(1-e)=0$. Can we deduced that for each idempotent $e $ of $R $ either $s^me=0$ or $s^m(1-e)=0$ for a fix natUral number $m $?