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
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 (N:M) is maximal is R S,
then N is a prime submodule of M.