Locally nilpotent derivations with a PID ring of constants

Abstract

Let K \mathcal {K} be a commutative field of characteristic zero, A \mathcal {A} be a domain containing K \mathcal {K} and ∂ \partial be a locally nilpotent K \mathcal {K} -derivation of A \mathcal {A} . We give in this paper a description of the differential K \mathcal {K} -algebra ( A , ∂ ) (\mathcal {A},\partial ) under the assumptions that the ring of constants A ∂ \mathcal {A}^{\partial } of ∂ \partial is a PID, ∂ \partial is fixed point free and its special fibers are reduced.