Geodesic
Criteria of semisimplicity of skew polynomial ring
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 701-709 
V. A. Mushrub. Criteria of semisimplicity of skew polynomial ring. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 701-709. http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a8/
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     title = {Criteria of semisimplicity of skew polynomial ring},
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     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $R$ be an associative ring and $f$ be an injective endomorphism of $R$ such that the Cohn–Jordan extension $A(R,f)$ satisfies the ascending chain condition on left annihilators. In this paper we obtain some semiprimitivity criteria for the skew polynomial ring $R[x,f]$ over the ring $R$. In particular, we prove that the skew polynomial ring is semisimple if and only if its prime radical is zero. Furthermore, it is so if and only if the ring $R$ is semiprime.

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