In this paper we give a further study on fully prime submodules. For any fully prime submodules we define a product called $\am$-product. The further investigation of fully prime submodules in this work, i.e. the fully m-system and fully prime radicals, is related to this product. We show that the fully prime radical of any submodules can be characterize by the fully m-system. As a special case, the fully prime radical of a module $M$ is the intersection of all minimal fully prime submodules of $M$.