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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.


References [Enhancements On Off] (What's this?)

  • 1. A. van den Essen, Polynomial automorphisms and the Jacobian conjecture, Progress in Mathematics, vol. 190, Birkhäuser Verlag, Basel, 2000. MR 1790619 (2001j:14082)
  • 2. G. Freudenburg, Algebraic theory of locally nilpotent derivations, Encyclopaedia of Mathematical Sciences, vol. 136, Springer, 2006. MR 2259515 (2008f:13049)
  • 3. Sh. Kaliman and M. Zaidenberg, Affine modifications and affine hypersurfaces with a very transitive automorphism group, Transform. Groups 4 (1999), no. 1, 53-95. MR 1669174 (2000f:14099)
  • 4. M. Miyanishi, Curves on rational and unirational surfaces, Tata Institute of Fundamental Research, Lectures on Mathematics and Physics, vol. 60, Tata Institute of Fundamental Research, Bombay, 1978. MR 546289 (81f:14001)
  • 5. -, $ \mathbb{G}\sb a$-actions and completions, J. Algebra 319 (2008), no. 7, 2845-2854. MR 2397411 (2009d:14087)
  • 6. -, Additive group scheme actions on integral schemes defined over discrete valuation rings, J. Algebra 322 (2009), no. 9, 3331-3344. MR 2567423
  • 7. D. L. Wright, On the Jacobian Conjecture, Illinois J. Math 25 (1981), no. 3, 423-440. MR 620428 (83a:12032)

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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.

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