MODULE-THEORETIC CHARACTERIZATIONS OF KRULL DOMAINS

Title & Authors
MODULE-THEORETIC CHARACTERIZATIONS OF KRULL DOMAINS
Kim, Hwan-Koo;

Abstract
The following statements for an infra-Krull domain $\small{R}$ are shown to be equivalent: (1) $\small{R}$ is a Krull domain; (2) for any essentially finite $\small{w}$-module $\small{M}$ over $\small{R}$, the torsion submodule $\small{t(M)}$ of $\small{M}$ is a direct summand of $\small{M}$; (3) for any essentially finite $\small{w}$-module $\small{M}$ over $\small{R}$, $\small{t(M){\cap}pM=pt(M)}$, for all maximal $\small{w}$-ideal $\small{p}$ of $\small{R}$; (4) $\small{R}$ satisfies the $\small{w}$-radical formula; (5) the $\small{R}$-module $\small{R{\oplus}R}$ satisfies the $\small{w}$-radical formula.
Keywords
Krull domain;infra-Krull domain;strong Mori domain;$\small{w}$-radical formula;
Language
English
Cited by
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