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Fundamentalnaya i Prikladnaya Matematika, 1995, Volume 1, Issue 3, Pages 701–709
(Mi fpm98)
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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.
Received: 01.01.1995
Citation:
V. A. Mushrub, “Criteria of semisimplicity of skew polynomial ring”, Fundam. Prikl. Mat., 1:3 (1995), 701–709
Linking options:
https://www.mathnet.ru/eng/fpm98 https://www.mathnet.ru/eng/fpm/v1/i3/p701
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