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ON THE CONNECTION BETWEEN DIFFERENTIAL POLYNOMIAL RINGS AND POLYNOMIAL RINGS OVER NIL RINGS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 101 / Issue 3 / June 2020
- Published online by Cambridge University Press:
- 16 September 2019, pp. 438-441
- Print publication:
- June 2020
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- Article
- Export citation
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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.
