Some results on S-SFT modules

Let [Formula: see text] be a commutative ring with nonzero identity element, [Formula: see text] a multiplicatively closed subset of [Formula: see text] and [Formula: see text] an [Formula: see text]-module. This paper is devoted to introduce and study the concept of [Formula: see text]-SFT module. The module [Formula: see text] is said to be [Formula: see text]-SFT if for each submodule [Formula: see text] of [Formula: see text], there exist [Formula: see text], an integer [Formula: see text] and a finitely generated submodule [Formula: see text] of [Formula: see text] such that [Formula: see text] for every [Formula: see text] and [Formula: see text]. We show that this concept shares many good properties with those of [Formula: see text]-Noetherian and SFT modules. We study the Cohen-type theorem for [Formula: see text]-SFT modules. Also, we study the transfer of the [Formula: see text]-SFT variant to direct product, homomorphic image[Formula: see text]. We give several characterizations of [Formula: see text]-SFT modules. Many examples and counterexamples are given.