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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 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.

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UDC: 512.552.16

Citation: V. A. Mushrub, “Criteria of semisimplicity of skew polynomial ring”, Fundam. Prikl. Mat., 1:3 (1995), 701–709

Citation in format AMSBIB
\Bibitem{Mus95} \by V.~A.~Mushrub \paper Criteria of semisimplicity of skew polynomial ring \jour Fundam. Prikl. Mat. \yr 1995 \vol 1 \issue 3 \pages 701--709 \mathnet{http://mi.mathnet.ru/fpm98} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1788551} \zmath{https://zbmath.org/?q=an:0866.16018}