Some Results of Fully Prime Submodules

A fully invariant submodule of is called fully prime in if for fully invariant submodules and of , implies or with [ 11 ]. In this paper, we give some characterizations of fully prime submodules. We, among other results, show that every fully prime submodule of a self-generator right -module contains a minimal fully prime submodule. We also study the endomorphisms ring of fully prime modules. We show that the endomorphisms ring of fully prime quasi-projective modules are prime.