Article
| Title: | $b$-generalized skew derivations acting on Lie ideals in prime rings (English) |
| Author: | Dhara, Basudeb |
| Author: | Singh, Kalyan |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 575-597 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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 $K$. (English) |
| Keyword: | derivation |
| Keyword: | $b$-generalized derivation |
| Keyword: | $b$-generalized skew derivation |
| Keyword: | Lie ideal |
| Keyword: | prime ring |
| MSC: | 16N60 |
| MSC: | 16W25 |
| DOI: | 10.21136/CMJ.2024.0507-23 |
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| Date available: | 2024-07-10T14:57:29Z |
| Last updated: | 2024-07-15 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152459 |
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