Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MODULE-THEORETIC CHARACTERIZATIONS OF KRULL DOMAINS

  • Kim, Hwan-Koo (Department of Information Security Hoseo University)
  • Received : 2011.02.16
  • Published : 2012.05.31
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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 $R$, $t(M){\cap}pM=pt(M)$, for all maximal $w$-ideal $p$ of $R$; (4) $R$ satisfies the $w$-radical formula; (5) the $R$-module $R{\oplus}R$ satisfies the $w$-radical formula.

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References

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