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Normal Pairs of Going-down Rings
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  • Journal title : Kyungpook mathematical journal
  • Volume 51, Issue 1,  2011, pp.1-10
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2011.51.1.001
 Title & Authors
Normal Pairs of Going-down Rings
Dobbs, David Earl; Shapiro, Jay Allen;
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 Abstract
Let (R, T) be a normal pair of commutative rings (i.e., R 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 S 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.
 Keywords
Normal pair;prime ideal;total quotient ring;valuation domain;divided domain;pullback;going-down ring;EGD ring;locally divided ring;weak Baer ring;reduced ring;
 Language
English
 Cited by
1.
Characterizing the ring extensions that satisfy FIP or FCP, Journal of Algebra, 2012, 371, 391  crossref(new windwow)
2.
A GENERALIZATION OF PRÜFER'S ASCENT RESULT TO NORMAL PAIRS OF COMPLEMENTED RINGS, Journal of Algebra and Its Applications, 2011, 10, 06, 1351  crossref(new windwow)
3.
On Finite Maximal Chains of Weak Baer Going-Down Rings, Communications in Algebra, 2012, 40, 5, 1843  crossref(new windwow)
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