Nearly small semi-prime sub-modules

Suppose that D is an unitary module over a ring that is commutative F, with identity. A non-zero sub-module N of D called as nearly small semi-prime, if for every t ∈ F, m ∈ D,(m) be small of M and t2 m ∈ N, which implies that tm ∈ N + Rad(D) and an F-module M is a nearly small semi-prime module, if (0) is a nearly small semi-prime sub-module. In this work, We investigate the characteristics and properties of these types of sub modules (modules).