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

Nikhilesh Dasgupta; Animesh Lahiri

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

Commutative Algebra 2025-03-11 v5

Authors: Nikhilesh Dasgupta , Animesh Lahiri

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.

Keywords

image ideals nice derivations quasi-nice derivations ufd polynomial ring generators

Cite

@article{arxiv.2302.13787,
  title  = {On image ideals of nice and quasi-nice derivations over a UFD},
  author = {Nikhilesh Dasgupta and Animesh Lahiri},
  journal= {arXiv preprint arXiv:2302.13787},
  year   = {2025}
}

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