On finite generation of kernels of locally nilpotent R-derivations of R[X,Y,Z]

Bhatwadekar, S. M. ; Daigle, Daniel (2009) On finite generation of kernels of locally nilpotent R-derivations of R[X,Y,Z] Journal of Algebra, 322 (9). pp. 2915-2926. ISSN 0021-8693

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00218...

Related URL: http://dx.doi.org/10.1016/j.jalgebra.2008.05.003

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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Locally Nilpotent Derivations; Hilbert Fourteenth Problem
ID Code:3232
Deposited On:11 Oct 2010 09:55
Last Modified:16 May 2016 14:04

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