DefinePK

Abstract

Let R be an associative ring with identify and M
be a unital left R-module. A proper submodule N of M is called
prime if whenever r R, m M and rRm
N, then m N or rM N .
In this paper we show the following two result. i The prime avoidance theorem
for unital left modules over noncommutative rings. ii Let S be an m
150 system subset of a ring R and S be an S system
subset of an R- module M. Let N be a submodule of M which
is maximal in M-S. if the ideal NM is maximal is R 150 S,
then N is a prime submodule of M.