Generalized derivations acting on Lie ideals in prime rings and Banach algebras
Let $R$ be a prime ring and $L$ a non-central Lie ideal of $R.$ The purpose of this paper is to describe generalized derivations of $R$ satisfying some algebraic identities locally on $L.$ More precisely, we consider two generalized derivations $F_1$ and $F_2$ of a prime ring $R$ satisfying one of t...
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Ivan Franko National University of Lviv
2023-09-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/394 |
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| author | A. Hermas L. Oukhtite L. Taoufiq |
| author_facet | A. Hermas L. Oukhtite L. Taoufiq |
| author_sort | A. Hermas |
| collection | DOAJ |
| description | Let $R$ be a prime ring and $L$ a non-central Lie ideal of $R.$ The purpose of this paper is to describe generalized derivations of $R$ satisfying some algebraic identities locally on $L.$ More precisely, we consider two generalized derivations $F_1$ and $F_2$ of a prime ring $R$ satisfying one of the following identities:
1. $F_1(x)\circ y +x \circ F_2(y) =0,$
2. $[F_1(x),y] + F_2([x,y]) =0,$
for all $x,y$ in a non-central Lie ideal $L$ of $R.$ Furthermore, as an application, we study continuous generalized derivations satisfying similar algebraic identities with power values on nonvoid
open subsets of a prime Banach algebra $A$. Our topological approach is based on Baire's
category theorem and some properties from functional analysis. |
| format | Article |
| id | doaj-art-745d2154658b4f1094d181ff8e70ccf9 |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2023-09-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-745d2154658b4f1094d181ff8e70ccf92025-08-20T03:28:41ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202023-09-0160131110.30970/ms.60.1.3-11394Generalized derivations acting on Lie ideals in prime rings and Banach algebrasA. Hermas0L. Oukhtite1L. Taoufiq2Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University Fez, MoroccoUniversity Sidi Mohamed Ben Abdella, FèsNational School of Applied Sciences, Ibn Zohr University Agadir, MoroccoLet $R$ be a prime ring and $L$ a non-central Lie ideal of $R.$ The purpose of this paper is to describe generalized derivations of $R$ satisfying some algebraic identities locally on $L.$ More precisely, we consider two generalized derivations $F_1$ and $F_2$ of a prime ring $R$ satisfying one of the following identities: 1. $F_1(x)\circ y +x \circ F_2(y) =0,$ 2. $[F_1(x),y] + F_2([x,y]) =0,$ for all $x,y$ in a non-central Lie ideal $L$ of $R.$ Furthermore, as an application, we study continuous generalized derivations satisfying similar algebraic identities with power values on nonvoid open subsets of a prime Banach algebra $A$. Our topological approach is based on Baire's category theorem and some properties from functional analysis.http://matstud.org.ua/ojs/index.php/matstud/article/view/394prime rings; lie ideals; generalized derivations; banach algebras |
| spellingShingle | A. Hermas L. Oukhtite L. Taoufiq Generalized derivations acting on Lie ideals in prime rings and Banach algebras Математичні Студії prime rings; lie ideals; generalized derivations; banach algebras |
| title | Generalized derivations acting on Lie ideals in prime rings and Banach algebras |
| title_full | Generalized derivations acting on Lie ideals in prime rings and Banach algebras |
| title_fullStr | Generalized derivations acting on Lie ideals in prime rings and Banach algebras |
| title_full_unstemmed | Generalized derivations acting on Lie ideals in prime rings and Banach algebras |
| title_short | Generalized derivations acting on Lie ideals in prime rings and Banach algebras |
| title_sort | generalized derivations acting on lie ideals in prime rings and banach algebras |
| topic | prime rings; lie ideals; generalized derivations; banach algebras |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/394 |
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