NEAR-RINGS OF HOMOGENEOUS MAPS

Abstract

Given an R-module V, the near-ring of homogeneous maps M_R(V) is the set of maps {f: V → V |f(rv) = rf(v) for all r b.epsis; R and v b.epsis; V} endowed with point-wise addition and composition of functions as multiplication. Modules with the property that M_R (V) = End _R(V) and those with the property that M_R (V) is a ring, will be characterized in certain cases. It will also be investigated whether these are local properties.