A Note ont-SFT-rings

We define a nonzero ideal A of an integral domain R to be a t-SFT-ideal if there exist a finitely generated ideal B ⊆ A and a positive integer k such that a k ∊ B v for each a ∊ A t , and a domain R to be a t-SFT-ring if each nonzero ideal of R is a t-SFT-ideal. This article presents a number of basic properties and stability results for t-SFT-rings. We show that an integral domain R is a Krull domain if and only if R is a completely integrally closed t-SFT-ring; for an integrally closed domain R, R is a t-SFT-ring if and only if R[X] is a t-SFT-ring; if R is a t-SFT-domain, then t − dim R[[X]] ≥ t − dim R. We also give an example of a t-SFT Prüfer v-multiplication domain R such that t − dim R[[X]] > t − dim R.