# AAR12

Let $x\,$ be a nilpotent element of the commutative ring $R\,$. Let $x^m=0\,$ for minimal $m\isin \mathbb{Z}^+\,$. Prove that $rx\,$ is nilpotent for all $r\isin R\,$.

$(rx)^m=r^mx^m=r^m\cdot 0=0\,$

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