Generalized derivations on Lie ideals and power values on prime rings

Year, pages: 2015, 975 - 980

Let $R$ be a non-commutative prime ring of characteristic different from $2$, $U$ the Utumi quotient ring of $R$, $C$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$, $G$ a non-zero generalized derivation of $R$. If $[G(u),u]ⁿ=[G(u),u]$, for all $u\in L$, with $n>1$, then one of the following holds: (1) $R$ satisfies the standard identity $s₄(x₁,...,x₄)$ and there exist $a\in U$ and $α\in C$ such that $G(x)=ax+xa+α x$ for all $x \in R$; (2) there exists $γ \in C$ such that $G(x)=γ x$ for all $x\in R$.

Scudo, G., Ansari, A. 2015. Generalized derivations on Lie ideals and power values on prime rings. In Mathematica Slovaca, vol. 65, no.5, pp. 975-980. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0066

Scudo, G., Ansari, A. (2015). Generalized derivations on Lie ideals and power values on prime rings. Mathematica Slovaca, 65(5), 975-980. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0066