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 $r$is 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.