Ascending Nets of Prüfer V-Multiplication Domains

Abstract

Let D be an integral domain, S ⊆ D a multiplicative set such that aD S ∩ D is a principal ideal for each a ∈ D and let D (S) = ⋃ s∈S D[X/s]. It is known that if D is a Prüfer v-multiplication domain (resp., generalized GCD domain, GCD domain), then so is D (S) respectively. When D is a Noetherian domain, we obtain a similar result for the power series analog D ((S)) = ⋃ s∈S D[[X/s]] of D (S). Our approach takes care simultaneously of both cases D (S) and D ((S)).