Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

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.

Module-theoretic characterizations of Krull domains

Hwankoo Kim

Hoseo University

Abstract

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