No CrossRef data available.
Published online by Cambridge University Press: 16 September 2019
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.
The authors are supported in part by NSF grant DMS 1653002.