Generalized epimorphism theorem

Abstract

Let R[X, Y] be a polynomial ring in two variables over a commutative ringR and let F∈ R[X, Y] such that R[X, Y]/(F)=R[Z] (a polynomial ring in one variable). In this set-up we prove that R[X, Y]= R[F, G] for some G ∈R[X, Y] if either R contains a field of characteristic zero or R is a seminormal domain of characteristic zero.