A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ring - Omaima Alshanqiti; Ashutosh Pandey; Mani Shankar Pandey (AIMS Mathematics)
This paper investigates the analysis of $ b $-generalized skew derivations, denoted as $ Δ_1 $ and $ Δ_2 $, within a prime ring $ \mathcal{R} $ with characteristic different from 2. Here, $ \mathcal{Q}_r $ represents the right Martindale quotient ring of $ \mathcal{R} $, and $ \mathcal{C} $ denoted its extended centroid. Additionally, $ \mathcal{L} $ is a noncentral Lie ideal of $ \mathcal{R} $. Assuming $ Δ_1 $ and $ Δ_2 $ are nontrivial $ b $-generalized skew derivations associated with the same automorphism $ α $, the paper aims to explore the detailed structure of these generalized derivations that satisfy the specific equation: \begin{document}$ p u Δ_1(u) + Δ_1(u) u q = Δ_2(u^2), \ \text{with} \ p + q \notin \mathcal{C}, \; \; \text{for all } u \in \mathcal{L}. $\end{document} The above-studied result generalized the already existing results [1,2] in the literature.