Throughout this paper, all rings have the identity 1 and ring homomorphisms are assumed to preserve 1. We use p to denote a prime integer and F to denote a field of characteristic p. For an element α in F, we set
A = F[ϰ]/(ϰp
- α)F[ϰ].
Moreover, by D and R, we denote the derivation of A induced by the ordinary derivation of F[ϰ] and the skew polynomial ring A[X,D] where aX = Xa+D(a) (a ∈ A), respectively (cf. [2]).
In [3], R. W. Gilmer determined all the B-automorphisms of B[X] for any commutative ring B. Since then, some extensions or generalizations of his results have been obtained ([1], [2] and [5]). As to the characterization of automorphisms of skew polynomial rings, M. Rimmer [5] established a thorough result in case of automorphism type, while M. Ferrero and K. Kishimoto [2], among others, have made some progress in case of derivation type.