MMN-1529
An identity with derivations in prime rings
Shuliang Huang;Abstract
Let $R$ be a prime ring with center $Z(R)$, and $d$ a derivation of $R$.
Suppose that $(d[x, y]_k)^n-m[x, y]_k\in Z(R)$ for all
$x, y \in R$, where $m\neq n, k \geq 1$ are fixed integers. Then $d=0$ or $R$ satisfies $s_4$, the standard identity in four variables. In the case $(d[x, y]_k)^n-m[x, y]_k=0$ for all
$x, y \in R$, then $d=0$ or $R$ is commutative.
Vol. 19 (2018), No. 2, pp. 899-905