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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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Bibliographic databases:
UDC: 512.552.16
Received: 01.01.1995

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}


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  • Фундаментальная и прикладная математика
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