Small 2-prime sub-modules

For an D-module (abbreviated D-mod) W and a commutative ring (with identity) D. we introduce the notion of small 2-prime sub-module (S-2-P sub-module; for short ) as a generalization of 2-prime sub-module. We prove many properties for this kind of submodules, among these results we prove if V s proper sub-module of a module W over a ring D, then V is small 2-prime sub-module if and only if [V:W (d)] = V is a small 2-prime submodule of W, for each d ∈ DD and d2∈[V:D W].