Around the Abhyankar--Sathaye Conjecture
A «rational» version of the strengthened form of the Commuting Derivation Conjecture, in which the assumption of commutativity is dropped, is proved. A systematic method of constructing in any dimension greater than $3$ the examples answering in the negative a question by M. El Kahoui is developed.
2010 Mathematics Subject Classification: Primary 14R10; Secondary 14R20, 14L30, 20G15.
Keywords and Phrases: Coordinate, locally nilpotent derivation, affine algebraic group, action, orbit.
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