summary:Let $R$ be a prime ring of characteristic different from 2, $Q_r$ its right Martindale quotient ring and $C$ its extended centroid. Suppose that $F$, $G$ are generalized skew derivations of $R$ with the same associated automorphism $\alpha $, and $p(x_1,\ldots ,x_n)$ is a non-central polynomial over $C$ such that $$ [F(x),\alpha (y)]=G([x,y]) $$ for all $x,y \in \{p(r_1,\ldots ,r_n)\colon r_1,\ldots ,r_n \in R\}$. Then there exists $\lambda \in C$ such that $F(x)=G(x)=\lambda \alpha (x)$ for all $x\in R$.
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机译：摘要：让$ R $是与2不同的特征素环，$ Q_r $是其右Martindale商环，$ C $是其扩展质心。假设$ F $，$ G $是$ R $的广义偏导数，具有相同的相关自同构$ \ alpha $，而$ p（x_1，\ ldots，x_n）$是超过C $的非中心多项式，例如对于所有$ x，y \ in \ {p（r_1，\ ldots，r_n）\冒号r_1，\，$$ [F（x），\ alpha（y）] = G（[x，y]）$$ ldots，r_n \ in R \} $。然后在C $中存在$ \ lambda \，使得对于R $中的所有$ x \ $ F（x）= G（x）= \ lambda \ alpha（x）$。
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