Nice derivations over principal ideal domains
Journal of Pure and Applied Algebra
In this paper we investigate to what extent the results of Z. Wang and D. Daigle on “nice derivations” of the polynomial ring k[X,Y,Z] over a field k of characteristic zero extend to the polynomial ring R[X,Y,Z] over a PID R, containing the field of rational numbers. One of our results shows that the kernel of a nice derivation on k[X1,X2,X3,X4] of rank at most three is a polynomial ring over k.
Dasgupta, Nikhilesh and Gupta, Neena, "Nice derivations over principal ideal domains" (2018). Journal Articles. 1149.