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- W4320169972 abstract "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 $deg(D) leqslant 3$. 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 $deg(D) leqslant 3$." @default.
- W4320169972 created "2023-02-13" @default.
- W4320169972 creator A5051495079 @default.
- W4320169972 date "2022-02-25" @default.
- W4320169972 modified "2023-10-01" @default.
- W4320169972 title "Some results on homogeneous locally nilpotent $R$-derivations on $R[X,Y,Z]$" @default.
- W4320169972 doi "https://doi.org/10.48550/arxiv.2202.12630" @default.
- W4320169972 hasPublicationYear "2022" @default.
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