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JOURNALS // Fundamentalnaya i Prikladnaya Matematika // Archive

Fundam. Prikl. Mat., 1995 Volume 1, Issue 3, Pages 701–709 (Mi fpm98)

Criteria of semisimplicity of skew polynomial ring

V. A. Mushrub

Moscow State Pedagogical University

Abstract: 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.

UDC: 512.552.16

Received: 01.01.1995



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