Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.12630 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $k$ be a field of characteristic zero and $R$ a $k$-algebra. In this paper we study homogeneous $R$-lnds $D$ on $R[X,Y,Z]$ with respect to the standard weights $(1,1,1)$. We show that when $R$ is a PID, $rank(D)$ can be at most $2$ if $°(D) \leqslant 3$. As a consequence we obtain a certain class of homogeneous lnds on $k^{[4]}$ whose kernel is $k^{[3]}$. Further when $R$ is a Dedekind domain, we give a bound for minimum number of generators of $\ker(D)$ as an $R$-algebra if $°(D) \leqslant 3$.