# On image ideals of nice and quasi-nice derivations over a UFD

## TL;DR

This paper characterizes the image ideals of certain derivations on polynomial rings over a UFD, providing explicit generators for these ideals in the context of nice and quasi-nice derivations.

## Contribution

It introduces a set of generators for the image ideals of irreducible nice and quasi-nice derivations over polynomial rings with a UFD base.

## Key findings

- Explicit generators for image ideals of nice derivations
- Extension of results to quasi-nice derivations
- Applicable to polynomial rings over UFDs

## Abstract

In this paper, for a field $k$ of characteristic zero and a finitely generated $k$-algebra $R$, we give a set of generators for the image ideals of irreducible nice and quasi-nice $R$-derivations on the polynomial ring $R[X,Y]$, where $R$ is a UFD.