Add to ORKGLet R be a ring. A proper submodule K of an 72-module M is called prime if whenever r ∈ R, m ∈ M and rRm ⊆ K then m ∈ K or rM ⊆ K. It is clear that prime submodules generalize the usual notion of prime ideals. The radical of a submodule N of M, denoted by radM(N) is defined to be the intersection of all prime submodules of M containing N. Now let R be a commutative ring. Let 7 be an ideal of R, As is well known, the radical of 7, defined as the intersection of all prime ideals containing 7, has the characterization √I = {r ∈ R : rn ?∈ I, for some n ∈ Z+}. A natural question arises, whether there is a somewhat similar characterization for the radical of a submodule, in particular, a characterization in which the knowledge of prime submodules...