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In this paper, we introduce the notion of S-M-cyclic submodules, which is a generalization of the notion of M-cyclic submodules. Let M, N be right R-modules and S be a multiplicatively closed subset of a ring R. A submodule A of N is said to be an S-M-cyclic submodule, if there exist s S and f HomR (M, N) such that As f (M) A. Besides giving many properties of S-M-cyclic submodules, we generalize some results on M-cyclic submodules to S-M-cyclic submodules. Furthermore, we generalize some properties of principally injective modules and pseudo-principally injective modules to S-principally injective modules and S-pseudo-principally injective modules, respectively. We study the transfer of this notion to various contexts of these modules.
Samruam Baupradist (Tue,) studied this question.
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