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

Title & Authors
LOCALLY PSEUDO-VALUATION DOMAINS OF THE FORM D[X]Nv
Chang, Gyu-Whan;

Abstract
Let D be an integral domain, X an indeterminate over D, $\small{N_v = \{f{\in}D[X]|(A_f)_v=D\}.}$. Among other things, we introduce the concept of t-locally PVDs and prove that $\small{D[X]N_v}$ 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 $\small{D[X]N_v}$ is a locally PVD.
Keywords
pseudo-valuation domain (PVD);(t-)locally PVD;UMT-domain;the ring $\small{D{[X]_{N}}_{v}}$;
Language
English
Cited by
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Korean Journal of Mathematics, 2010. vol.18. 2, pp.185-193
3.
*-NOETHERIAN DOMAINS AND THE RING D[X]N*, II,;

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1.
*-NOETHERIAN DOMAINS AND THE RING D[X]N*, II, Journal of the Korean Mathematical Society, 2011, 48, 1, 49
2.
PrÜfer-Like Domains and the Nagata Ring of Integral Domains, Communications in Algebra, 2011, 39, 11, 4246
3.
ON ALMOST PSEUDO-VALUATION DOMAINS, II, Korean Journal of Mathematics, 2011, 19, 4, 343
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