Correction to: “Commutants of some Hausdorff matrices”

Abstract

V be a valuation ring having a proper prime ideal P which is not branched; then P = \J λGΛ M λ , where {M x } λeΛ is the collection of prime ideals of V which are properly contained in P. In this case, P F[[X]]-P[[X]] if and only if (*) given any countable subcollection {M λ .} of {M λ }, (JΓ=i M λ. c P. Proof. Assuming (•), let f{X) = ΣΓ-oΛX' e P[[X]]. For each i, fie Mλ. for some λ* e A. Let pe P, pi US=oM~λ .; since pg Mλ. 9 it follows that fie Mλ. S (p)V for each i and f(X) e (p)V[[X]] S P F[[Z]]. Conversely, assuming that (*) fails, let {JJίiJlLj. be a countable subcollection of {M λ } XeΛ such that UΓ=i M λ. = P. By extracting a subsequence of {MjJ, we may assume that M λ .c:Mχ i+1 for each i.