Bulletin of the
Korean Mathematical Society BKMS

Let $R$ be a prime ring, $H$ a generalized derivation of $R$ and $L$ a noncommutative Lie ideal of $R$. Suppose that $u^sH(u)u^t=0$ for all $u \in L$, where $s\geq 0, t\geq 0$ are fixed integers. Then $H(x)=0$ for all $x\in R$ unless char$R=2$ and $R$ satisfies $S_4$, the standard identity in four variables.

Keywords: prime ring, derivation, generalized derivation, extended centroid, Utumi quotient ring

MSC numbers: 16W25, 16N60, 16R50