ON ALMOST PSEUDO-VALUATION DOMAINS, II

Abstract

Let D be an integral domain, D^w be the w-integral closure of D, X be an indeterminate over D, and N_v = {f ∈ D[X]|c(f)_v = D}. In this paper, we introduce the concept of t-locally APVD. We show that D is a t-locally APVD and a UMT- domain if and only if D is a t-locally APVD and Dw is a PvMD, if and only if D[X] is a t-locally APVD, if and only if D[X]Nv is a locally APVD.