대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제49권3호
  • /
  • Pages.601-608
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  • 2012
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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MODULE-THEORETIC CHARACTERIZATIONS OF KRULL DOMAINS

  • Kim, Hwan-Koo (Department of Information Security Hoseo University)
  • 투고 : 2011.02.16
  • 발행 : 2012.05.31
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초록

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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참고문헌

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