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Czechoslovak Mathematical Journal, Vol. 74, No. 2, pp. 575-597, 2024

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

Basudeb Dhara, Kalyan Singh

Received November 15, 2023.   Published online June 6, 2024.
Abstract:  Let $R$ be any noncommutative prime ring of ${\rm char}(R)\neq2,3$, $L$ 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: (1) $F(x)=\lambda x$ for all $x\in R$ and for some $\lambda\in C$, where $C$ is the extended centroid of $R$; (2) $R\subseteq M_2(K)$, the algebra of $2\times2$ matrices over a field $K$.
Keywords:  derivation; $b$-generalized derivation; $b$-generalized skew derivation; Lie ideal; prime ring
Classification MSC:  16W25, 16N60
DOI:  10.21136/CMJ.2024.0507-23
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Affiliations:   Basudeb Dhara (corresponding author), Department of Mathematics, Belda College, Belda, Deuli, Paschim Medinipur, 721424, West Bengal, India, e-mail: basu_dhara@yahoo.com; Kalyan Singh, Department of Mathematics, Jadavpur University, Jadavpur, Kolkata, 700032, West Bengal, India, e-mail: kalyank4singh@gmail.com
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