Generalized derivations and commuting additive maps on multilinear polynomials in prime rings

  • Filippis V. De
  • B. Dhara
  • G. Scudo


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 $R$.
How to Cite
DeF. V., DharaB., and ScudoG. “Generalized Derivations and Commuting Additive maps on Multilinear Polynomials in Prime Rings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 2, Feb. 2016, pp. 183-01,
Research articles