On generalized $(θ,φ)$-derivations in semiprime rings with involution

Year, pages: 2012, 451 - 460

The main purpose of this paper is to prove the following result: Let $R$ be a $2$-torsion free semiprime $*$-ring. Suppose that $θ$, $φ$ are endomorphisms of $R$ such that $θ$ is onto. If there exists an additive mapping $F: R \rightarrow R$ associated with a $(θ, φ)$-derivation $d$ of $R$ such that $F(xx^*)=F(x)θ(x^*)+φ(x)d(x^*)$ holds for all $x \in R$, then $F$ is a generalized $(θ,φ)$-derivation. Further, some more related results are obtained.

Ashraf, M., Rehman, N., Ali, S., Mozumder, M. 2012. On generalized $(θ,φ)$-derivations in semiprime rings with involution. In Mathematica Slovaca, vol. 62, no.3, pp. 451-460. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0021-1

Ashraf, M., Rehman, N., Ali, S., Mozumder, M. (2012). On generalized $(θ,φ)$-derivations in semiprime rings with involution. Mathematica Slovaca, 62(3), 451-460. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0021-1