Differential Operator Rings for Which Homogeneous Functions are Linear

Let e be the collection of those rings S such that, for every S-module V and every homogeneous function ƒ. V → V, ƒ(sv) = sƒ(v), s ∈ S, v ∈ V, ƒ is linear on V. In this paper we characterize those Stanley-Reisner rings, R, such that D(R) is in e.