  Let S be an m-system of a ring R, and P a submodule of a right R-module M.
This paper, presents the notion of S-prime submodule and provides some
properties and equivalent definitions. We define S-multiplication right module,
and prove that in multiplication (S-multiplication) right R-module M, the ideal
(P :_R M) is a right S-prime ideal of R if and only if P is an S-prime
submodule of M. Moreover, we give an S-version of prime avoidance lemma.
Furthermore, we define S-finite and S-Noetherian right modules following the
definitions in [1]. We prove that a multiplication finitely generated right
R-module M is S-Noetherian if (N :_R M) is an S-prime ideal of R, for all
submodules N of M. In addition, we give some examples of right S-Noetherian
rings.
