Annihilators of skew derivations with Engel conditions on prime rings
Articles > Article · 2019
Authors: Taylan Pehlivan, Emine ALBAŞ
Czechoslovak Mathematical Journal, Journal Indexed in SCI Expanded, International, WoS, 2019, vol 70, pp 587-603
DOI: 10.21136/cmj.2019.0412-18
Summary
summary: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 $a=0$.