On the semiprimitivity of free skew extensions of rings

Abstract

Let $X$ be a set of noncommuting variables of cardinality $card(X)⩾2$, and $\mathcal{G}=\{{\sigma }_x{\}}_{x\in X}$, $\mathcal{D}=\{{\delta }_x{\}}_{x\in X}$ be families of automorphisms and skew derivations of the ring $R$. It is proved that if the ring $R$ is semiprime Goldie, then the free skew extension $R[X;\mathcal{G},\mathcal{D}]$ is semiprimitive.

arXiv commentv3, final. To appear in Journal of Pure and Applied Algebra