MMN-779
Notes on generalized derivations of *-prime rings
Abstract
Let $(R,\ast)$ be a $2$-torsion free $\ast$-prime ring with involution $\ast$,
$U \neq0$ be a square closed $\ast$-Lie ideal of $R$. An additive mapping
$F:R\rightarrow R$ is called an generalized derivation if there exits a
derivation $d:R\rightarrow R$ such that $F(xy)=F(x)y+xd(y)$. In the present
paper, we shall show that $U \subseteq Z$ such that $R$ is a $\ast$-prime ring
admits a generalized derivation satisfying severeal condition but associated
with a derivation commuting with $\ast$.
Vol. 15 (2014), No. 1, pp. 117-123