On a residual coordinate which is a non-trivial line
Journal of Pure and Applied Algebra
Let k be an infinite field of positive characteristic p>2 and R denote the non-seminormal Noetherian local ring R=k[[t2,t3]]. In this note, we construct an example of a polynomial F in R[X,Y] such that R[X,Y]/(F) is isomorphic to the polynomial ring R[T] and F is a residual coordinate in R[X,Y], and yet F is not a coordinate in R[X,Y]. A modification of the above example shows that the Generalized Epimorphism Theorem of S.M. Bhatwadekar cannot be extended to an arbitrary Noetherian domain of characteristic zero.
Asanuma, Teruo and Dutta, Amartya Kumar, "On a residual coordinate which is a non-trivial line" (2021). Journal Articles. 2026.