R - مقاسات جزئية اولية من النمط

Abstract

Abstract.  is a commutative ring with unity.  is a sub-module of a non- zero left R-module , In this paper, first we define the notion of residual of a Sub-module in D  which is an ideal in a ring  and then we obtain some related results. In particular ,we state and prove some proposition. We need in this paper some concepts as multiplication  module , prime sub-module and an injective envelope . Finally we will introduce a new concept “ prime sub-module “. In this paper concepts of prime sub-modules and some other notions will be studied, as well as the relationship between properties of prime sub-modules  and other sub-modules . we will be studied image of  prime sub-module . Also  the relationship between the properties of prime sub-modules and other sub-modules.