Title: Nice derivations over principal ideal domains,
Abstract: In this paper we investigate to what extent the results of Z. Wang and D.
Daigle on nice derivations of the polynomial ring in three variables over a
field k of characteristic zero extend to the polynomial ring over a PID R,
containing the field of rational numbers. One of our results shows that the
kernel of a nice derivation on the polynomial ring in four variables over k of
rank at most three is a polynomial ring over k.