$b$-generalized skew derivations acting on Lie ideals in prime rings

Dhara, Basudeb ; Singh, Kalyan

Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 575-597

Abstract (VO)

Let $R$ be any noncommutative prime ring of ${\rm char}(R)\neq 2,3$, $L$ a noncentral Lie ideal of $R$ and $F$, $G$ two nonzero $b$-generalized skew derivations of $R$. Suppose that $$[F(u),u]G(u)=0$$ for all $u\in L$. Then at least one of the following conclusions holds: \item {(1)} $F(x)=\lambda x$ for all $x\in R$ and for some $\lambda \in C$, where $C$ is the extended centroid of $R$; \item {(2)} $R\subseteq M_2(K)$, the algebra of $2\times 2$ matrices over a field $K$.

Détail

DOI : 10.21136/CMJ.2024.0507-23

Classification : 16N60, 16W25
Keywords: derivation; $b$-generalized derivation; $b$-generalized skew derivation; Lie ideal; prime ring

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