2-prime submodules of modules

Abstract

Let R be a commutative ring with unity. And let E be a unitary R-module. Thispaper introduces the notion of 2-prime submodules as a generalized concept of 2-prime ideal, where proper submodule H of module F over a ring R is said to be 2-prime if , for r R and x F implies that or [ ]. we prove manyproperties for this kind of submodules, Let H is a submodule of module F over a ringR then H is a 2-prime submodule if and only if [N] is a 2-prime submodule ofE, where r R. Also, we prove that if F is a non-zero multiplication module, then [K:F] [H: F] for every submodule k of F such that H K. Furthermore, we will studythe basic properties of this kind of submodules.