Resumen de On Open Ring Pairs Of Commutative Rings

R. Douglas Chatham, David E. Dobbs

• If T is an integral commutative extension of a ring R such that R is an open ring, R[a, b] is a going-down ring for each a, b in T and T is semiquasilocal, then each ring contained between R and T is an open ring. An example is given to show that the "semiquasilocal" hypothesis cannot be deleted. If T is a commutative ring containing a ring R such that R[a, b] is an open ring for each a, b in T, then (R, T) is an INC-pair (equivalently, a residually algebraic pair).