ON THE CONNECTION BETWEEN DIFFERENTIAL POLYNOMIAL RINGS AND POLYNOMIAL RINGS OVER NIL RINGS

摘要

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.