Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4587400 | Journal of Algebra | 2009 | 12 Pages |
Abstract
Let R be a noetherian domain containing the field of rationals. We show that if R is Dedekind then the kernel of any locally nilpotent R-derivation of R[X,Y,Z] is a finitely generated R-algebra. Conversely, we show that if R is neither a field nor a Dedekind domain then there exists a locally nilpotent R-derivation of R[X,Y,Z] whose kernel is not finitely generated over R.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory