Generalized derivations with power values on rings and Banach algebras
Let $R$ be a prime ring and $I$ a nonzero ideal of $R.$ The purpose of this paper is to classify generalized derivations of $R$ satisfying some algebraic identities with power values on $I.$ More precisely, we consider two generalized derivations $F$ and $H$ of $R$ satisfying one of the following id...
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Institute of Mathematics of the Czech Academy of Science
2024-12-01
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| Series: | Mathematica Bohemica |
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| Online Access: | https://mb.math.cas.cz/full/149/4/mb149_4_3.pdf |
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| author | Abderrahman Hermas Abdellah Mamouni Lahcen Oukhtite |
| author_facet | Abderrahman Hermas Abdellah Mamouni Lahcen Oukhtite |
| author_sort | Abderrahman Hermas |
| collection | DOAJ |
| description | Let $R$ be a prime ring and $I$ a nonzero ideal of $R.$ The purpose of this paper is to classify generalized derivations of $R$ satisfying some algebraic identities with power values on $I.$ More precisely, we consider two generalized derivations $F$ and $H$ of $R$ satisfying one of the following identities: \begin{itemize} \item[(1)] $aF(x)^mH(y)^m=x^ny^n$ for all $x,y \in I,$ \item[(2)] $ (F(x)\circ H(y))^m=(x\circ y)^n$ for all $x,y \in I,$ \end{itemize} for two fixed positive integers $m\geq1$, $n\geq1$ and $a$ an element of the extended centroid of $R$. Finally, as an application, the same identities are studied locally on nonvoid open subsets of a prime Banach algebra. |
| format | Article |
| id | doaj-art-1521761c1d394826b001095683a0eeea |
| institution | OA Journals |
| issn | 0862-7959 2464-7136 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj-art-1521761c1d394826b001095683a0eeea2025-08-20T02:19:33ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362024-12-01149449150210.21136/MB.2024.0079-23MB.2024.0079-23Generalized derivations with power values on rings and Banach algebrasAbderrahman HermasAbdellah MamouniLahcen OukhtiteLet $R$ be a prime ring and $I$ a nonzero ideal of $R.$ The purpose of this paper is to classify generalized derivations of $R$ satisfying some algebraic identities with power values on $I.$ More precisely, we consider two generalized derivations $F$ and $H$ of $R$ satisfying one of the following identities: \begin{itemize} \item[(1)] $aF(x)^mH(y)^m=x^ny^n$ for all $x,y \in I,$ \item[(2)] $ (F(x)\circ H(y))^m=(x\circ y)^n$ for all $x,y \in I,$ \end{itemize} for two fixed positive integers $m\geq1$, $n\geq1$ and $a$ an element of the extended centroid of $R$. Finally, as an application, the same identities are studied locally on nonvoid open subsets of a prime Banach algebra.https://mb.math.cas.cz/full/149/4/mb149_4_3.pdf prime ring generalized derivation banach algebra jacobson radical |
| spellingShingle | Abderrahman Hermas Abdellah Mamouni Lahcen Oukhtite Generalized derivations with power values on rings and Banach algebras Mathematica Bohemica prime ring generalized derivation banach algebra jacobson radical |
| title | Generalized derivations with power values on rings and Banach algebras |
| title_full | Generalized derivations with power values on rings and Banach algebras |
| title_fullStr | Generalized derivations with power values on rings and Banach algebras |
| title_full_unstemmed | Generalized derivations with power values on rings and Banach algebras |
| title_short | Generalized derivations with power values on rings and Banach algebras |
| title_sort | generalized derivations with power values on rings and banach algebras |
| topic | prime ring generalized derivation banach algebra jacobson radical |
| url | https://mb.math.cas.cz/full/149/4/mb149_4_3.pdf |
| work_keys_str_mv | AT abderrahmanhermas generalizedderivationswithpowervaluesonringsandbanachalgebras AT abdellahmamouni generalizedderivationswithpowervaluesonringsandbanachalgebras AT lahcenoukhtite generalizedderivationswithpowervaluesonringsandbanachalgebras |