On separable and H-separable polynomials in skew polynomial rings of several variables

Abstract

Let B be a ring with 1, and {ρ1,⋯,ρe} a set of automorphisms of B. Let B[X1,⋯,Xe;ρ1,⋯,ρe;{uij}] be the skew polynomial ring of automorphism type. In this paper, we shall give equivalent conditions that the residue ring of B[X1,⋯,Xe;ρ1,⋯,ρe;{uij}] by the ideal generated by a set {Xm11−u1,⋯,Xmee−ue} to be separable or H-separable over B.