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 is a generalized skew derivation of R, L a non-central Lie ideal of R, $a\in R$ a non-zero element of R, $m,r\ge 1$ and $s,t\ge 0$ fixed integers. If $a{(F(u{)}^r(F(u{)}^{s}u+uF(u{)}^s)F(u{)}^t)}^m=0$ for all $u\in L$, then either there exists $b\in Q_r$ such that $F(x)=bx$, for any $x\in R$, with ab = 0 or $R\subseteq M_2(K)$, the ring of $2\times 2$ matrices over a field K.

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关于李理想的广义偏斜推导和湮灭条件的幂值的方程

设R是特征不同于 2 的素环，${问}_r$它的右 Martindale 商环和C是它的扩展质心。假设F是R的广义偏斜导数，L是R的非中心李理想，$A\in R$R的非零元素，$米,r\ge \mathrm{1个}$和$秒,吨\ge 0$固定整数。如果$A{(F(你{)}^r(F(你{)}^{秒}你+你F(你{)}^{秒})F(你{)}^{吨})}^{米}=0$对全部$你\in \mathrm{大号}$, 那么要么存在$b\in {问}_r$这样$F(X)=bX$, 对于任何$X\in R$, ab  = 0 或$R\subseteq {米}_{\mathrm{2个}}(钾)$, 的环$\mathrm{2个}\times \mathrm{2个}$域K上的矩阵。