Abstract
Let $R$ be a ring with center $Z$ and $\alpha$, $\beta$ and $d$ mappings of $R$. A mapping $F$ of $R$ is called a centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivation associated with $d$ if $F(xy)-F(x)\alpha(y)-\beta(x)d(y)\in Z$ for all $x, y \in R$. The objective of the present paper is to study the following conditions: (i) $F(xy)\pm \beta(x)G(y)\in Z$, (ii) $F(xy)\pm g(x)\alpha(y)\in Z$ and (iii) $F(xy)\pm g(y)\alpha(x)\in Z$ for all $x,y$ in some appropriate subsets of $R$, where $G$ is a multiplicative $($generalized$)$-$(\alpha,\beta)$-derivation of $R$ associated with the map $g$ on $R$.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
