Radical formula and prime submodules

Let B be a submodule of an R-module M. The intersection of all prime submodules of M containing B is denoted by rad(B). For every positive integer n, a generalization of E(B) denoted by En(B) of M will be introduced. Moreover, E(B) En(B) rad(B). In this paper we will study the equality En(B) =rad(B). It is proved that if R is an arithmetical ring of finite Krull dimension n, then En(B) =rad(B).