On nonnil S-SFT rings

Let [Formula: see text] be a commutative ring with nonzero identity element and [Formula: see text] a multiplicative subset of [Formula: see text]. In this paper, we introduce and investigate the notion of nonnil [Formula: see text]-SFT rings. The ring [Formula: see text] is said to be nonnil [Formula: see text]-SFT, if for each nonnil-ideal [Formula: see text] of [Formula: see text], there exist [Formula: see text], [Formula: see text] and a finitely generated ideal [Formula: see text] such that [Formula: see text] for all [Formula: see text], in that case, the ideal [Formula: see text] is called [Formula: see text]-SFT. It is shown that the ring [Formula: see text] is nonnil [Formula: see text]-SFT ring if and only if each nonnil-prime ideal (disjoint with [Formula: see text]) is [Formula: see text]-SFT. The transfert of the nonnil [Formula: see text]-SFT concept to flat overrings and trivial extension is investigated. We give several characterizations of nonnil [Formula: see text]-SFT rings. Also, we give a characterization of the nonnil-SFT variant in terms of the nonnil [Formula: see text]-SFT variant.