Abstract
In this Paper we show the following: Let R be a prime ring (with characteristic different two) and a $\in$ R. Let Θ, $\phi$ : R longrightarrow R be automorphisms and let d : R longrightarrow R be a nonzero Θ-derivation. (i) if［d($\chi$), a］Θo$\phi$ = 0 (or d(［$\chi$, a］$\phi$ = 0) for all $\chi$ $\in$ R, then a+$\phi$(a) $\in$ Z, the conte. of R, (ii) if〈d($\chi$), a〉 = 0 for all $\chi$$\in$R, then d(a) =0. (iii) if [ad($\chi$), $\chi$］$\phi$= 0 for all $\chi$$\in$R, then either a = 0 or R is commutative.
