On almost pseudo-valuation domains, II
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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 D^w is a PvMD, if and only if D[X] is a t-locally APVD, if and only if D[X]_N_v is a locally APVD.
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 D^w is a PvMD, if and only if D[X] is a t-locally APVD, if and only if D[X]_N_v is a locally APVD.
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