Czechoslovak Mathematical Journal, Vol. 70, No. 2, pp. 587-603, 2020
Annihilators of skew derivations with Engel conditions on prime rings
Taylan Pehlivan, Emine Albas
Received September 21, 2018. Published online December 16, 2019.
Abstract: Let $R$ be a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ring $Q$, $C$ the extended centroid of $R$ and $a\in R$. Suppose that $\delta$ is a nonzero $\sigma$-derivation of $R$ such that $a[\delta(x^n),x^n]_k=0$ for all $x\in R$, where $\sigma$ is an automorphism of $R$, $n$ and $k$ are fixed positive integers. Then $a=0$.
Keywords: prime ring; derivation; skew derivation; automorphism