The SFT property and the ring R((X))

Abstract

An ideal I is called,in SFT-ideal if there exist a natural number n and a finitely generated ideal J subset of I such that x(n) is an element of J for each x is an element of I. An SFT-ring is a ring such that every ideal is an ideal SFT-ideal. For a commutative ring D, let D((X)) he the power series ring D parallel to X parallel to localized at the power series with unit content ideal. We. show that fora Prufer domain D, all the prime ideals of D((X),) are formally extended from D if and only if D((X)) is SFT if and only if D is SFT. (c) 2005 Elsevier B.V. All rights reserved.