MMN-1343
Generalization of generalized derivations acting as homomorphisms or anti-homomorphismswith central values on Lie ideals in prime rings
Abstract
Let $R$ be a prime ring of characteristic not $2$, $U$ a nonzero square closed Lie ideal of $R$ and $F,G,H$ be generalized derivations with associated derivations $d, \delta, h$ of $R$ respectively. In the present paper, we study the situations if one the follwoing holds (1) $F(u)G(v)\pm H(uv)\in Z(R)$, (2) $F(u)F(v)\pm H(vu)\in Z(R)$; for all $u,v\in U$, then $U\subseteq Z(R)$.
Vol. 16 (2015), No. 2, pp. 769-779
DOI: 10.18514/MMN.2015.1343