Jacobson Monoform Modules

In this paper, we introduce and study the concept of Jacobson monoform modules whichis a proper generalization of that of monoform modules. We present a characterization of semisimplerings in terms of Jacobson monoform modules by proving that a ring Ris semisimple if and only if every R-module is Jacobson monoform. Moreover, we demonstrate that over a ring R, the properties monoform, Jacobson monoform, compressible, uniform and weakly co-Hopfian are all equivalent.