Kyungpook Mathematical Journal

  • 제51권1호
  • /
  • Pages.1-10
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  • 2011
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Normal Pairs of Going-down Rings

  • 투고 : 2010.06.04
  • 심사 : 2010.12.09
  • 발행 : 2011.03.31
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⟨ 이전 논문 다음 논문 ⟩

초록

Let (R, T) be a normal pair of commutative rings (i.e., R ${\subseteq}$ T is a unita extension of commutative rings, not necessarily integral domains, such that S is integrally closed in T for each ring S such that R ${\subseteq}$ S ${\subseteq}$ T) such that the total quotient ring of R is a von Neumann regular ring. Let P be one of the following ring-theoretic properties: going-down ring, extensionally going-down (EGD) ring, locally divided ring. Then R has P if and only if T has P. An example shows that the "if" part of the assertion fails if P is taken to be the "divided domain" property.

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참고문헌

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피인용 문헌

  1. Characterizing the ring extensions that satisfy FIP or FCP vol.371, 2012, https://doi.org/10.1016/j.jalgebra.2012.07.055
  2. On Finite Maximal Chains of Weak Baer Going-Down Rings vol.40, pp.5, 2012, https://doi.org/10.1080/00927872.2011.558881
  3. A GENERALIZATION OF PRÜFER'S ASCENT RESULT TO NORMAL PAIRS OF COMPLEMENTED RINGS vol.10, pp.06, 2011, https://doi.org/10.1142/S021949881100521X