Representation of rings with faithful polyform modules

This article studies subrings which satisfy a density-type criterion called m-density. It is first observed that if V is a faithful quasiinjective R-module then R is an m-dense subring of BiendRV. This is used to obtain the main result which states that R is an m-dense subring of a direct product of rings of linear transformations if and only if R has a faithful locally finite dimensional module whose essential sub-modules are rational.