A Note on t-SFT-rings

Abstract

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.

Key Words:

• Power series ring
• t-dimension
• t-SFT-ideal
• t-SFT-ring

Mathematics Subject Classification:

• Primary 13C15, 13E99, 13F25
• Secondary 13A15, 13F05, 13F30

ACKNOWLEDGMENT

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2005-003-C00003).

Notes

Communicated by A. Facchini.