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UFDs with commuting linearly independent locally nilpotent derivations

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons44379

El Kahoui,  M'hammed
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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El Kahoui, M. (2005). UFDs with commuting linearly independent locally nilpotent derivations. Journal of Algebra, 289, 446-452.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-2827-5
Abstract
In this paper we study affine -UFDs of transcendence degree n without nonconstant units, having n-1 commuting linearly independent locally nilpotent -derivations. We prove in case n=2, and algebraically closed of characteristic zero, that such rings are polynomial rings in two variables over . We then show that the commuting derivations Conjecture is equivalent to a weak version of the Abhyankar–Sathaye Conjecture.