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arXiv · 1403.2230

Differential polynomial rings over rings satisfying a polynomial identity

Jason P. Bell·Blake W. Madill·Forte Shinko
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Abstract

Let $R$ be a ring satisfying a polynomial identity and let $δ$ be a derivation of $R$. We show that if $N$ is the nil radical of $R$ then $δ(N)\subseteq N$ and the Jacobson radical of $R[x;δ]$ is equal to $N[x;δ]$. As a consequence, we have that if $R$ is locally nilpotent then $R[x;δ]$ is locally nilpotent. This affirmatively answers a question of Smoktunowicz and Ziembowski.

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BibTeXRIS

Jason P. Bell, Blake W. Madill, Forte Shinko. 2014-06-17. Differential polynomial rings over rings satisfying a polynomial identity. https://doi.org/10.1016/j.jalgebra.2014.09.039

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