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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| Datum: | 2026 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9547 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1871646539320918016 |
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| author | Dhara, B. Tammam El-Sayiad, M. S. Dhara, B. Tammam El-Sayiad, M. S. |
| author_facet | Dhara, B. Tammam El-Sayiad, M. S. Dhara, B. Tammam El-Sayiad, M. S. |
| author_institution_txt_mv | [
{
"author": "B. Dhara",
"institution": "Department of Mathematics, Belda College, Belda, Paschim Medinipur, India"
},
{
"author": "M. S. Tammam El-Sayiad",
"institution": "Department of Mathematics and Computer Science Faculty of Science, Beni-Suef University, Beni-Suef city, Egypt"
}
] |
| author_sort | Dhara, B. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-07-24T15:24:12Z |
| description | 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 $\mathscr{H}.$ |
| doi_str_mv | 10.3842/umzh.v78i7-8.9547 |
| first_indexed | 2026-07-25T01:00:33Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9547 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-25T01:00:33Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-95472026-07-24T15:24:12Z Hyper-commuting generalized derivations acting on Lie ideals in prime rings Hyper-commuting generalized derivations acting on Lie ideals in prime rings Dhara, B. Tammam El-Sayiad, M. S. Dhara, B. Tammam El-Sayiad, M. S. Prime ring generalized derivation extended centroid Lie ideal Algebra 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 $\mathscr{H}.$ УДК 512.552 Гіперкомутуючі узагальнені диференціювання, що діють на ідеалах лі у простих кільцях Нехай $\mathscr{R}$ – просте кільце з кільцем часток Утумі $\mathscr{U}$ та розширеним центроїдом $\mathcal{C},$ $n\geq 1$ – фіксоване ціле число та ${\rm char}(\mathscr{R})\neq 2.$ Крім того, нехай $\mathscr{F}, \mathcal{G}$ та $\mathscr{H}$ – три узагальнені диференціювання кільця $\mathscr{R},$ а $\mathscr{L}$ – нецентральний ліївський ідеал кільця $\mathscr{R}.$ За умови $$\bigr[\mathscr{F}(\mathcal{G}(u)u)-u\mathscr{H}(u),u\bigr]_n=0$$ для всіх $u \in \mathscr{L}$ описано структуру відображень $\mathscr{F}, \mathcal{G}$ і $\mathscr{H}.$ Institute of Mathematics, NAS of Ukraine 2026-07-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9547 10.3842/umzh.v78i7-8.9547 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 7-8 (2026); 597–598 Український математичний журнал; Том 78 № 7-8 (2026); 597–598 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9547/10682 Copyright (c) 2026 B. Dhara, M. S. Tammam El-Sayiad |
| spellingShingle | Dhara, B. Tammam El-Sayiad, M. S. Dhara, B. Tammam El-Sayiad, M. S. Hyper-commuting generalized derivations acting on Lie ideals in prime rings |
| title | Hyper-commuting generalized derivations acting on Lie ideals in prime rings |
| title_alt | Hyper-commuting generalized derivations acting on Lie ideals in prime rings |
| title_full | Hyper-commuting generalized derivations acting on Lie ideals in prime rings |
| title_fullStr | Hyper-commuting generalized derivations acting on Lie ideals in prime rings |
| title_full_unstemmed | Hyper-commuting generalized derivations acting on Lie ideals in prime rings |
| title_short | Hyper-commuting generalized derivations acting on Lie ideals in prime rings |
| title_sort | hyper-commuting generalized derivations acting on lie ideals in prime rings |
| topic_facet | Prime ring generalized derivation extended centroid Lie ideal Algebra |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9547 |
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