For $n\ge 2$ and for a ring $R,$ the notation $P_n(R)$ means that $r^n-r$ is nilpotent for all $r\in R$. In this paper, rings $R$ for which $P_n(R)$ holds are completely characterized for any integers $n\ge 2$. This answers a question which was raised in [T. Kosan, Y. Zhou, T. Yildirim, Rings with $x^n-x$ nilpotent, J. Algebra Appl.19(4) (2020) 2050065].

中文翻译：

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在具有 xn − x 幂零的环上

为了$n\ge 2$和一个戒指$R,$符号${磷}_n(R)$意思是$r^n-r$对所有人都是幂零的$r\in R$. 在本文中，环$R$为此${磷}_n(R)$持有对于任何整数都是完全特征化的$n\ge 2$. 这回答了 [T. Kosan, Y. Zhou, T. Yildirim, 戒指$X^n-X$幂零，J.代数应用。19 (4) (2020) 2050065]。