0N Quasi and pseudo prime module

Abstract

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 ann_RN is a prime idal for every N be a submodule of a module M[2].And  M is called pseudo-prime  Module if ann_RN is primary ideal for every N be asubmodule of  A module M [3],[4],where where ann_RN={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