LOCALLY NILPOTENT DERIVATIONS OVER A UFD AND AN APPLICATION TO RANK 2LOCALLY NILPOTENT DERIVATIONS OF K[X-1,...,X-N]

Given a UFD R containing the rational numbers, we study locally nilpot ent R-derivations of the polynomial ring R[X, Y]; in particular, we gi ve a generalization of Rentschler's Theorem and a criterion for the ex istence of a slice. These results are then applied to describe rank tw o locally nilpotent derivations of k[X-1,...,X-n], where k is a field of characteristic zero. We also give an example of a nontriangulable l ocally nilpotent derivation of k[X,Y,Z] whose set of fixed points is a line. (C) 1998 Academic Press.