Jordan homoderivation behavior of generalized derivations in prime rings
UDC 512.5 Suppose that $R$ is a prime ring with ${\rm char}(R)\neq 2$ and $f(\xi_1,\ldots,\xi_n)$ is a noncentral multilinear polynomial over $C( = Z(U)),$ where $U$ is the Utumi quotient ring of $R.$ An additive mapping $h\colon R\rightarrow R$ is called homoderivation if $h(ab) = h(a)...
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| Datum: | 2023 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7241 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512632792940544 |
|---|---|
| author | Bera, Nripendu Dhara, Basudeb Bera, Nripendu Dhara, Basudeb |
| author_facet | Bera, Nripendu Dhara, Basudeb Bera, Nripendu Dhara, Basudeb |
| author_sort | Bera, Nripendu |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:34:39Z |
| description | UDC 512.5
Suppose that $R$ is a prime ring with ${\rm char}(R)\neq 2$ and $f(\xi_1,\ldots,\xi_n)$ is a noncentral multilinear polynomial over $C( = Z(U)),$ where $U$ is the Utumi quotient ring of $R.$ An additive mapping $h\colon R\rightarrow R$ is called homoderivation if $h(ab) = h(a)h(b)+h(a)b+ah(b)$ for all $a,b\in R.$ We investigate the behavior of three generalized derivations $F,$ $G,$ and $H$ of $R$ satisfying the condition $$F(\xi^2) = G(\xi)^2+H(\xi)\xi+\xi H(\xi)$$ for all $\xi \in f(R) = \{f(\xi_1,\ldots,\xi_n) \mid \xi_1,\ldots,\xi_n\in R\}.$ |
| doi_str_mv | 10.3842/umzh.v75i9.7241 |
| first_indexed | 2026-03-24T03:31:53Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7241 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:53Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-72412024-06-19T00:34:39Z Jordan homoderivation behavior of generalized derivations in prime rings Jordan homoderivation behavior of generalized derivations in prime rings Bera, Nripendu Dhara, Basudeb Bera, Nripendu Dhara, Basudeb Generalized derivation, Homoderivation, Utumi quotient ring, Extended centroid, Multilinear polynomial, Prime ring UDC 512.5 Suppose that $R$ is a prime ring with ${\rm char}(R)\neq 2$ and $f(\xi_1,\ldots,\xi_n)$ is a noncentral multilinear polynomial over $C( = Z(U)),$ where $U$ is the Utumi quotient ring of $R.$ An additive mapping $h\colon R\rightarrow R$ is called homoderivation if $h(ab) = h(a)h(b)+h(a)b+ah(b)$ for all $a,b\in R.$ We investigate the behavior of three generalized derivations $F,$ $G,$ and $H$ of $R$ satisfying the condition $$F(\xi^2) = G(\xi)^2+H(\xi)\xi+\xi H(\xi)$$ for all $\xi \in f(R) = \{f(\xi_1,\ldots,\xi_n) \mid \xi_1,\ldots,\xi_n\in R\}.$ УДК 512.5 Поведінка жорданової гомопохідної для узагальнених похідних на простих кільцях Припустимо, що $R$ – просте кільце з  ${\rm char}(R)\neq 2$, а $f(\xi_1,\ldots,\xi_n)$ – нецентральний мультилінійний поліном над $C( = Z(U)),$ де $U$ ---  фактор-кільце  Утумі $R.$ Адитивне відображення $h\colon R\rightarrow R$ називається гомопохідною, якщо $h(ab) = h(a)h(b)+h(a)b +ah(b)$ для всіх $a,b\in R.$ Досліджено поведінку трьох узагальнених похідних $F,$ $G$ та  $H$ на $R$, що задовольняють умову $$F(\xi^2) = G(\xi)^2+H(\xi)\xi+\xi H(\xi)$$ для всіх $\xi \in f(R) = \{f(\xi_1,\ldots,\xi_n) | \xi_1,\ldots,\xi_n\in R\}.$  Institute of Mathematics, NAS of Ukraine 2023-09-26 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7241 10.3842/umzh.v75i9.7241 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 9 (2023); 1178 - 1194 Український математичний журнал; Том 75 № 9 (2023); 1178 - 1194 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7241/9745 Copyright (c) 2023 Басудеб Дхара |
| spellingShingle | Bera, Nripendu Dhara, Basudeb Bera, Nripendu Dhara, Basudeb Jordan homoderivation behavior of generalized derivations in prime rings |
| title | Jordan homoderivation behavior of generalized derivations in prime rings |
| title_alt | Jordan homoderivation behavior of generalized derivations in prime rings |
| title_full | Jordan homoderivation behavior of generalized derivations in prime rings |
| title_fullStr | Jordan homoderivation behavior of generalized derivations in prime rings |
| title_full_unstemmed | Jordan homoderivation behavior of generalized derivations in prime rings |
| title_short | Jordan homoderivation behavior of generalized derivations in prime rings |
| title_sort | jordan homoderivation behavior of generalized derivations in prime rings |
| topic_facet | Generalized derivation Homoderivation Utumi quotient ring Extended centroid Multilinear polynomial Prime ring |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7241 |
| work_keys_str_mv | AT beranripendu jordanhomoderivationbehaviorofgeneralizedderivationsinprimerings AT dharabasudeb jordanhomoderivationbehaviorofgeneralizedderivationsinprimerings AT beranripendu jordanhomoderivationbehaviorofgeneralizedderivationsinprimerings AT dharabasudeb jordanhomoderivationbehaviorofgeneralizedderivationsinprimerings |