(untitled) (Journal of the College of Basic Education, 2023)
We shall study the new relation between two the quasi-prime module and pseudo-prime module .The purpose of this paper is to study and gave the new relation between the two different prime module Introduction: We shall study the new relation between two different prime modules. A module is called Quasi-prime module if annRN is a prime idal for every N be a submodule of a module M[2].And M is called pseudo-prime Module if annRN is primary ideal for every N be asubmodule of A module M [3],[4],where where annRN=r R;rx=0 for each x N. The primary goal of this paper to give some cond ition to show That there is some relation between the Quasi-prime modules and pseudo Prime modules.In the start we show that every Quasi-prime modules is Pseudo-prime modules but the converse is not true in general unless M be cyclic .And we showing that if N is pseudo-prime submodule of M then the R-homomorphism -1(N) is also pseudo-prime Submodule of M .And we prove if N is a pseudo-prime submodule of M and is an epimorphism such that ker N then (N) is a pseudo prime submodule of M