Let Rbe any ring with unit and M be a left R-module. As we already know, any left R-module is also a right S-module, where  such that Mis an -bimodule. A multiplication   R-module is a module Mwhich each submodule Nhas the form IM, for some ideal Iin R. We study such a multiplication module over its endomorphism ring and call it a fully multiplication module. Moreover, we investigate the properties of the multiplication defined in this module, related to the left residuals, annihilators and its fully prime submodules. The main results are the necessary and sufficient conditions for a fully multiplication module to be a fully prime module.

-bimodules, fully multiplication modules, fully prime submodules, annihilators, left residuals.