Let $R$ be a prime ring with the extended centroid $C$ and $L$ a noncentral Lie ideal of $R$. Suppose that $a\in R$, $\gamma \in C$ and $d$ is a derivation of $R$ such that $a\left(\right.d{(u^2)}^s-\gamma u^{2t}{\left)\right.}^m\in C$ for all $u\in L$, where $s,t,m$ are fixed positive integers. If $\gamma \ne 0$ or $d\ne 0$, then $a=0$ unless $R\subseteq M_2(F)$, the $2\times 2$ matrix ring over a field $F$. This result gives an affirmative answer to the open conjecture recently raised by Huang in [Derivations with annihilator conditions on Lie ideals in prime rings, J. Algebra Appl. 19 (2020) 2050025].

中文翻译：

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质数环李理想导数幂值的歼灭者

让$R$是质心延长的素环$C$和$\mathrm{大号}$的非中心李理想$R$. 假设$\mathrm{一个}\in R$,$\gamma \in C$和$d$是一个推导$R$这样$\mathrm{一个}\left(\right.d{({你}^2)}^s-\gamma {你}^{2吨}{\left)\right.}^{米}\in C$对所有人$你\in \mathrm{大号}$， 在哪里$s,吨,米$是固定的正整数。如果$\gamma \ne 0$或者$d\ne 0$， 然后$\mathrm{一个}=0$除非$R\subseteq {米}_2(F)$， 这$2\times 2$场上的矩阵环$F$. 这一结果对 Huang 最近在 [Derivations with annihilator conditions on Lie Ideals in prime ring, J. Algebra Appl.  ] 中提出的开放猜想给出了肯定的回答。19（2020）2050025]。