Power Series Rings Over Prüfer v-multiplication Domains. II

Abstract

AbstractLet D be an integral domain, X1(D) be the set of height-one prime ideals of D, {Xβ} and {Xα} be two disjoint nonempty sets of indeterminates over D, D[{Xβ}] be the polynomial ring over D, and D[{Xβ}][[{Xα}]]1 be the first type power series ring over D[{Xβ}]. Assume that D is a Prüfer v-multiplication domain (PvMD) in which each proper integral t-ideal has only finitely many minimal prime ideals (e.g., t-SFT PvMDs, valuation domains, rings of Krull type). Among other things, we show that if X1(D) = Ø or DP is a DVR for all P ∊ X1(D), then D[{Xβ}][[{Xα}]]1D−{0} is a Krull domain. We also prove that if D is a t-SFT PvMD, then the complete integral closure of D is a Krull domain and ht(M[{Xβ}][[{Xα}]]1) = 1 for every height-one maximal t-ideal M of D.