On Abhyankar-Sathaye Conjecture for a family of linear hypersurfaces in ₊⁴

Let k be a field. In this paper we study the Abhyankar-Sathaye Epimorphism Conjecture for certain hyperplanes in ₖ⁴ defined by a polynomial of the form a (X) Y-F (X, Z, T). When k=, Kaliman, V\'en\'ereau and Zaidenberg have proved that such hyperplanes are rectifiable in ⁴_. We extend their result over any field of characteristic zero and when k is a field of arbitrary characteristic we prove the Abhyankar-Sathaye Conjecture for such hyperplanes under some conditions on the roots of a (X).