Journal of the
Korean Mathematical Society JKMS

Let $D$ be an integral domain, $X$ an indeterminate over $D$, $N_v = \{f \in D[X]| (A_f)_v = D\}$. Among other things, we introduce the concept of $t$-locally PVDs and prove that $D[X]_{N_v}$ is a locally PVD if and only if $D$ is a $t$-locally PVD and a UMT-domain, if and only if $D[X]$ is a $t$-locally PVD, if and only if each overring of $D[X]_{N_v}$ is a locally PVD.

Keywords: pseudo-valuation domain (PVD), ($t$-)locally PVD, UMT-domain, the ring $D[X]_{N_v}$

MSC numbers: 13A15, 13B25, 13F05, 13G05