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Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 1998; 35(2): 259-268

Printed June 1, 1998

Copyright © The Korean Mathematical Society.

Prufer $v$-multiplication domains in which each $t$-ideal is divisorial

Chul Ju Hwang and Gyu Whan Chang

Silla University, Postech

Abstract

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We give several characterizations of a TV-PVMD and we show that the localization $R[X;S]_{N_v}$ of a semigroup ring $R[X;S]$ is a TV-PVMD if and only if $R$ is a TV-PVMD where $N_v=\{f \in R[X]| (A_f)_v=R \}$ and $S$ is a torsion free cancellative semigroup with zero.

Keywords: a divisorial ideal, $t$-ideal, PVMD, TV-domain, an independent ring of Krull type, semigroup ring

MSC numbers: 13A15

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