TY - JOUR
AU - Filippis V. De
AU - B. Dhara
AU - G. Scudo
PY - 2016/02/25
Y2 - 2023/06/09
TI - Generalized derivations and commuting additive maps
on multilinear polynomials in prime rings
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 68
IS - 2
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1833
AB - 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 $R$.
ER -