HOMOGENEOUS FUNCTIONS DETERMINED BY CYCLIC SUBMODULES

Abstract

For a unital module V over a commutative ring R, let C denote the collection of cyclic submodules. The ring ϵ_R(V;C) = {f ε End_R V |f(C) ⊆C, ∀C ε_R (V;C) has been the object of several recent studies in which the structure of ϵ_R(V;C) is related to the triple (V, R,C). Here we introduce a new ring H_R(V;C) containing ϵ(V;C) and investigate its structure in terms of the parameters (V, R, C).