A note on t-SFT-rings

Abstract

We define a nonzero ideal Lambda of an integral domain R to be a t-SFT-ideal if there exist a finitely generated ideal B subset of A and a positive integer k such that a(k) epsilon B-v for each a epsilon 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 R[[X]]. We also give an example of a t-SFT v-multiplication domain R such that t-dim R [[X]] > t-dim R.