Let $ℛ$ be a prime ring, ${𝒬}_r$ the right Martindale quotient ring of $ℛ$ and $𝒞$ the extended centroid of $ℛ$. In this paper, we discuss the relationship between the structure of prime rings and the behavior of skew derivations on multilinear polynomials. More precisely, we investigate the m-potent commutators of skew derivations involving multilinear polynomials, i.e.,

中文翻译：

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涉及偏导数和多线性多项式的m-势能交换子

让 $ℛ$ 成为素环， ${𝒬}_{\mathrm{[R}}$ 右马丁代尔商环 $ℛ$ 和 $𝒞$ 的扩展质心 $ℛ$。在本文中，我们讨论了质数环的结构与多元线性多项式上的偏导数的行为之间的关系。更准确地说，我们研究了涉及多元线性多项式的偏导数的m-势能交换子，即