UFDs with commuting linearly independent locally nilpotent derivations

Abstract

In this paper we study affine K -UFDs of transcendence degree n without nonconstant units, having n − 1 commuting linearly independent locally nilpotent K -derivations. We prove in case n = 2 , and K algebraically closed of characteristic zero, that such rings are polynomial rings in two variables over K . We then show that the commuting derivations Conjecture is equivalent to a weak version of the Abhyankar–Sathaye Conjecture.