| Title:
|
Generalized derivations with power values on rings and Banach algebras (English) |
| Author:
|
Hermas, Abderrahman |
| Author:
|
Mamouni, Abdellah |
| Author:
|
Oukhtite, Lahcen |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
4 |
| Year:
|
2024 |
| Pages:
|
491-502 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $m\geq 1$, $n\geq 1$ 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. (English) |
| Keyword:
|
prime ring |
| Keyword:
|
generalized derivation |
| Keyword:
|
Banach algebra |
| Keyword:
|
Jacobson radical |
| MSC:
|
16N60 |
| MSC:
|
16W25 |
| MSC:
|
46J10 |
| DOI:
|
10.21136/MB.2024.0079-23 |
| . |
| Date available:
|
2024-12-13T19:04:52Z |
| Last updated:
|
2024-12-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152676 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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