Commun. Korean Math. Soc. 2018; 33(1): 73-83
Online first article July 13, 2017 Printed January 31, 2018
https://doi.org/10.4134/CKMS.c170127
Copyright © The Korean Mathematical Society.
Motoshi Hongan, Nadeem ur Rehman
, Aligarh Muslim University
Let $R$ be an associative ring with involution $\ast$ and $\alpha, \beta: R\rightarrow R$ ring homomorphisms. An additive mapping $d:R\rightarrow R$ is called an $(\alpha, \beta)^\ast$-derivation of $R$ if $d(xy)=d(x)\alpha(y^\ast)+\beta(x)d(y)$ is fulfilled for any $x,y \in R$, and an additive mapping $F:R\rightarrow R$ is called a generalized $(\alpha, \beta)^\ast$-derivation of $R$ associated with an $(\alpha, \beta)^\ast$-derivation $d$ if $F(xy)=F(x)\alpha(y^\ast)+\beta(x)d(y)$ is fulfilled for all $x,y \in R$. In this note, we intend to generalize a theorem of Vukman \cite{V}, and a theorem of Daif and El-Sayiad \cite{DS}, moreover, we generalize a theorem of Ali et al.~\cite{AFFK} and a theorem of Huang and Koc \cite{HK} related to generalized Jordan triple $(\alpha, \beta)^\ast$-derivations.
Keywords: semiprime rings, Lie ideals, $(\alpha,\beta)^\ast$-derivations, generalized $(\alpha,\beta)^\ast$-derivations, Jordan $(\alpha, \beta)^\ast$-derivations, generalized Jordan $(\alpha, \beta)^\ast$-derivations
MSC numbers: 16W25, 16N60, 16U80
2017; 32(3): 535-542
2012; 27(3): 441-448
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd