Generalized derivations with power values on rings and Banach algebras

Abderrahman Hermas; Abdellah Mamouni; Lahcen Oukhtite

Mathematica Bohemica (2024)

  • Volume: 149, Issue: 4, page 491-502
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Hermas, Abderrahman, Mamouni, Abdellah, and Oukhtite, Lahcen. "Generalized derivations with power values on rings and Banach algebras." Mathematica Bohemica 149.4 (2024): 491-502. <http://eudml.org/doc/299633>.

@article{Hermas2024,
abstract = {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.},
author = {Hermas, Abderrahman, Mamouni, Abdellah, Oukhtite, Lahcen},
journal = {Mathematica Bohemica},
language = {eng},
number = {4},
pages = {491-502},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized derivations with power values on rings and Banach algebras},
url = {http://eudml.org/doc/299633},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Hermas, Abderrahman
AU - Mamouni, Abdellah
AU - Oukhtite, Lahcen
TI - Generalized derivations with power values on rings and Banach algebras
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 4
SP - 491
EP - 502
AB - 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.
LA - eng
UR - http://eudml.org/doc/299633
ER -

References

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