#### Title

On a residual coordinate which is a non-trivial line

#### Article Type

Research Article

#### Publication Title

Journal of Pure and Applied Algebra

#### Abstract

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.

#### DOI

10.1016/j.jpaa.2020.106523

#### Publication Date

4-1-2021

#### Recommended Citation

Asanuma, Teruo and Dutta, Amartya Kumar, "On a residual coordinate which is a non-trivial line" (2021). *Journal Articles*. 2026.

https://digitalcommons.isical.ac.in/journal-articles/2026