LAUSR

Abstract An Artin–Schreier covering of the affine plane is a hypersurface in A 3 defined by an equation z p − z = f ( x , y ) . Modeling on hypersurfaces of this type, we consider in the present article a normal affine domain B with a G : = Z / p Z -action which is written in the form B = A [ z ] , z p − s z = a with s , a ∈ A , where A = B G is the G-invariant subring. We also prove a classification result of Z / p Z -actions on the affine plane A 2 = Spec k [ x , y ] , which was first announced by S. Kuroda.