Abstract
Let $R$ be a noncommutative prime ring and $a\in R$. Suppose that $f$ is a right generalized $\beta$-derivation of $R$ such that $a[f(x),x]_k=0$ for all $x\in R$, where $k$ is a fixed positive integer. Then $a=0$ or there exists $s\in C$ such that $f(x)=sx$ for all $x\in R$ except when $R=M_2(GF(2))$.
Citation
Jui-Chi Chang. "GENERALIZED SKEW DERIVATIONS WITH ANNIHILATING ENGEL CONDITIONS." Taiwanese J. Math. 12 (7) 1641 - 1650, 2008. https://doi.org/10.11650/twjm/1500405076
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