Hyper-commuting generalized derivations acting on Lie ideals in prime rings
UDC 512.552 Let $\mathscr{R}$ be a prime ring with its Utumi ring of quotients $\mathscr{U}$ and extended centroid $\mathcal{C}.$ Also let $n\geq 1$ be a fixed integer and let ${\rm char}(\mathscr{R})\neq 2.$ Suppose that $\mathscr{F}, \mathcal{G},$ and $\mathscr{H}$ are three generalized derivation...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9547 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 512.552
Let $\mathscr{R}$ be a prime ring with its Utumi ring of quotients $\mathscr{U}$ and extended centroid $\mathcal{C}.$ Also let $n\geq 1$ be a fixed integer and let ${\rm char}(\mathscr{R})\neq 2.$ Suppose that $\mathscr{F}, \mathcal{G},$ and $\mathscr{H}$ are three generalized derivations of $\mathscr{R}$ and $\mathscr{L}$ is a noncentral Lie ideal of $\mathscr{R}.$ If $$\bigr[\mathscr{F}(\mathcal{G}(u)u)-u\mathscr{H}(u),u\bigr]_n=0$$ for all $u \in \mathscr{L},$ then we describe the structure of the maps $\mathscr{F}, \mathcal{G},$ and $\mathscr{H}.$ |
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| DOI: | 10.3842/umzh.v78i7-8.9547 |