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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241628 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590734700576768 |
|---|---|
| author | Omaima Alshanqiti Ashutosh Pandey Mani Shankar Pandey |
| author_facet | Omaima Alshanqiti Ashutosh Pandey Mani Shankar Pandey |
| author_sort | Omaima Alshanqiti |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3393e2df8ecc423f8f3722114f5706e5 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-3393e2df8ecc423f8f3722114f5706e52025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912341843420410.3934/math.20241628A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ringOmaima Alshanqiti0Ashutosh Pandey1Mani Shankar Pandey2Department of Mathematics, Umm Al-Qura University, Makkah, Saudi ArabiaDepartment of Mathematics and Statistics, Manipal University Jaipur, Jaipur, Rajasthan 303007, IndiaDepartment of Sciences, Indian Institute of Information Technology Design and Manufacturing Kurnool, Andhra Pradesh 518008, IndiaThis 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}. $\end{document} The above-studied result generalized the already existing results [1,2] in the literature.https://www.aimspress.com/article/doi/10.3934/math.20241628prime ringslie idealsright martindale quotient ring$ \mathrm{b} $-generalized skew derivationextended centroid |
| spellingShingle | Omaima Alshanqiti Ashutosh Pandey Mani Shankar Pandey A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ring AIMS Mathematics prime rings lie ideals right martindale quotient ring $ \mathrm{b} $-generalized skew derivation extended centroid |
| title | A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ring |
| title_full | A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ring |
| title_fullStr | A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ring |
| title_full_unstemmed | A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ring |
| title_short | A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ring |
| title_sort | characterization of b generalized skew derivations on a lie ideal in a prime ring |
| topic | prime rings lie ideals right martindale quotient ring $ \mathrm{b} $-generalized skew derivation extended centroid |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241628 |
| work_keys_str_mv | AT omaimaalshanqiti acharacterizationofbgeneralizedskewderivationsonalieidealinaprimering AT ashutoshpandey acharacterizationofbgeneralizedskewderivationsonalieidealinaprimering AT manishankarpandey acharacterizationofbgeneralizedskewderivationsonalieidealinaprimering AT omaimaalshanqiti characterizationofbgeneralizedskewderivationsonalieidealinaprimering AT ashutoshpandey characterizationofbgeneralizedskewderivationsonalieidealinaprimering AT manishankarpandey characterizationofbgeneralizedskewderivationsonalieidealinaprimering |