• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1405-1416
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• 2008

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.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.281-284
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• 1996

In this paper we characterize strongly prime ideals and prove a theorem: an integral domain R is a PVD if and only if every maximal ideal M of R is strongly prime.