A necessary and sufficient condition for triangulability of derivations of k[X, Y, Z] Original Research Article

We give a triangulability criterion for derivations of k[X, Y, Z]. As an application, we give an example of two locally nilpotent derivations D and T of k[X, Y, Z], where T is triangulable but D is not, with equality of the ideals of fixed points: (DX, DY, DZ) = (TX, TY, TZ).