Bull. Korean Math. Soc. 2012; 49(3): 601-608
Printed May 1, 2012
https://doi.org/10.4134/BKMS.2012.49.3.601
Copyright © The Korean Mathematical Society.
Hwankoo Kim
Hoseo University
The following statements for an infra-Krull domain $R$ are shown to be equivalent: (1) $R$ is a Krull domain; (2) for any essentially finite $w$-module $M$ over $R$, the torsion submodule $t(M)$ of $M$ is a direct summand of $M$; (3) for any essentially finite $w$-module $M$ over $R$, $t(M) \cap \mathfrak{p}M = \mathfrak{p}t(M)$, for all maximal $w$-ideal $\mathfrak{p}$ of $R$; (4) $R$ satisfies the $w$-radical formula; (5) the $R$-module $R \oplus R$ satisfies the $w$-radical formula.
Keywords: Krull domain, infra-Krull domain, strong Mori domain, $w$-radical formula
MSC numbers: Primary 13F05; Secondary 13A15, 13C13
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