2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63154Let R be a regular ring essentially of finite type over a perfect field k. An R-module M is called a unit R[F]-module if it comes equipped with an isomorphism F*M-->M where F denotes the Frobenius map on Spec R, and F* is the associated pullback functor. It is well known that M then carries a natural D-module structure. In this paper we investigate the relation between the unit R[F]-structure and the induced D-structure on M. In particular, it is shown that, if k is algebraically closed and M is a simple finitely generated unit R[F]-module, then it is also simple as a D-module. An example showing the necessity of k being algebraically closed is also given.25 pages. Some minor changes following referee's suggestion. To appear in Trans. AMSAlgebraic GeometryCommutative Algebra13A35; 16S99text