@article{De_Dhara_Scudo_2016, title={Generalized derivations and commuting additive maps
on multilinear polynomials in prime rings}, volume={68}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1833}, abstractNote={Let $R$ be a prime ring with characteristic different from $2, U$ be its right Utumi quotient ring, $C$ be its extended centroid, $F$ and $G$ be additive maps on $R$ , $f(x_1, ..., x_n)$ be a multilinear polynomial over $C$, and $I$ be a nonzero right ideal of $R$ .
We obtain information about the structure of $R$ and describe the form of $F$ and $G$ in the following cases:
$$(1) [(F^2 + G)(f(r_1, ..., r_n)), f(r_1, ..., r_n)] = 0$$ for all $r_1, . . . , r_n \in R$, where $F$ and $G$ are generalized derivations of $R$ ;
$$(2) [(F^2 + G)(f(r_1, ..., r_n)), f(r_1, ..., r_n)] = 0$$for all $r_1, ..., r_n \in I$, where $F$ and $G$ are derivations of $R$.}, number={2}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={De, Filippis V. and Dhara, B. and Scudo, G.}, year={2016}, month={Feb.}, pages={183-201} }