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

An ideal I is called an SFT-ideal if there exist a natural number n   and a finitely generated ideal J⊆IJ⊆I such that xn∈Jxn∈J for each x∈Ix∈I. An SFT-ring is a ring such that every ideal is an SFT-ideal. For a commutative ring DD, let D((X))D((X)) be the power series ring D[[X]]D[[X]] localized at the power series with unit content ideal. We show that for a Prüfer domain DD, all the prime ideals of D((X))D((X)) are formally extended from DD if and only if D((X))D((X)) is SFT if and only if DD is SFT.