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Normal Pairs of Going-down Rings
2011
Kyungpook Mathematical Journal
Let (R, T ) be a normal pair of commutative rings (i.e., R ⊆ T is a unital 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
doi:10.5666/kmj.2011.51.1.001
fatcat:4zgviwpkijcjrpxoj65fgtfeky