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arXiv · 1408.5112

On the Jacobson radical of skew polynomial extensions of rings satisfying a polynomial identity

Blake W. Madill
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Abstract

Let $R$ be a ring satisfying a polynomial identity and let $D$ be a derivation of $R$. We consider the Jacobson radical of the skew polynomial ring $R[x;D]$ with coefficients in $R$ and with respect to $D$, and show that $J(R[x;D])\cap R$ is a nil $D$-ideal. This extends a result of Ferrero, Kishimoto, and Motose, who proved this in the case when $R$ is commutative.

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Blake W. Madill. 2014-08-21. On the Jacobson radical of skew polynomial extensions of rings satisfying a polynomial identity. https://arxiv.org/abs/1408.5112

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