On the semiprimitivity of free skew extensions of rings

Let $X$ be a set of noncommuting variables of cardinality $card(X)\geqslant 2$,and${\mathscr G}={\sigma_x}{x\in X}$,${\mathscr D}={\delta_x}{x\in X}$befamiliesofautomorphismsandskewderivationsofthering$R$. It is proved that if the ring $R$ is semiprime Goldie, then the free skew extension $R[X;\mathcal{G},\mathcal{D}]$ is semiprimitive.