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http://dx.doi.org/10.4134/JKMS.2008.45.5.1405

LOCALLY PSEUDO-VALUATION DOMAINS OF THE FORM D[X]Nv  

Chang, Gyu-Whan (Department of Mathematics University of Incheon)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.5, 2008 , pp. 1405-1416 More about this Journal
Abstract
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 $D{[X]_{N}}_{v}$;
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