FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 3, PAGES 701-709

Criteria of semisimplicity of skew polynomial ring

V.A.Mushrub

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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