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Locally nilpotent derivations with a PID ring of constants


Authors: Moulay A. Barkatou and M’hammed El Kahoui
Journal: Proc. Amer. Math. Soc. 140 (2012), 119-128
MSC (2010): Primary 14R20
DOI: https://doi.org/10.1090/S0002-9939-2011-10962-6
Published electronically: May 25, 2011
MathSciNet review: 2833523
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Abstract: Let $ \mathcal{K}$ be a commutative field of characteristic zero, $ \mathcal{A}$ be a domain containing $ \mathcal{K}$ and $ \partial$ be a locally nilpotent $ \mathcal{K}$-derivation of $ \mathcal{A}$. We give in this paper a description of the differential $ \mathcal{K}$-algebra $ (\mathcal{A},\partial)$ under the assumptions that the ring of constants $ \mathcal{A}^{\partial}$ of $ \partial$ is a PID, $ \partial$ is fixed point free and its special fibers are reduced.


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Additional Information

Moulay A. Barkatou
Affiliation: Laboratoire XLIM, UMR 6172, CNRS-Université de Limoges, Avenue Albert-Thomas 123, 87060, Limoges Cedex, France
Email: moulay.barkatou@unilim.fr

M’hammed El Kahoui
Affiliation: Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, P.O. Box 2390, Marrakesh, Morocco
Email: elkahoui@ucam.ac.ma

DOI: https://doi.org/10.1090/S0002-9939-2011-10962-6
Keywords: Locally nilpotent derivation, Plinth ideal, affine modification
Received by editor(s): July 16, 2009
Received by editor(s) in revised form: November 11, 2010
Published electronically: May 25, 2011
Additional Notes: The second author was partially supported by the CNRST project URAC01
Communicated by: Ted Chinburg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.