Normal Pairs of Going-down Rings

David Earl Dobbs, Jay Allen Shapiro
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
more » ... assertion fails if P is taken to be the "divided domain" property.
doi:10.5666/kmj.2011.51.1.001 fatcat:4zgviwpkijcjrpxoj65fgtfeky