UFDs with commuting linearly independent locally nilpotent derivations

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