Abstract
In this paper, we study some connections between the polynomial ring $R[y]$ and the differential polynomial ring $R[x;D]$. In particular, we answer a question posed by Smoktunowicz, which asks whether $R[y]$ is nil when $R[x;D]$ is nil, provided that $R$ is an algebra over a field of positive characteristic and $D$ is a locally nilpotent derivation.
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