A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ring
This paper investigates the analysis of $ \mathrm{b} $-generalized skew derivations, denoted as $ \Delta_1 $ and $ \Delta_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 $ \ma...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241628 |
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| Summary: | This paper investigates the analysis of $ \mathrm{b} $-generalized skew derivations, denoted as $ \Delta_1 $ and $ \Delta_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 $ \Delta_1 $ and $ \Delta_2 $ are nontrivial $ \mathrm{b} $-generalized skew derivations associated with the same automorphism $ \alpha $, the paper aims to explore the detailed structure of these generalized derivations that satisfy the specific equation: \begin{document}$ p u \Delta_1(u) + \Delta_1(u) u q = \Delta_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. |
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| ISSN: | 2473-6988 |