Zero-Dimensional Subrings of a Product of Commutative Rings

Abstract

An extension of rings R T is said to be a zero-dimensional pair if all intermediate rings between R and T are zerodimensional. In this paper, we investigate the question of when a pair Q aPA R a ;Q aPA T a is zero-dimensional, where each R a ; T a is a zero-dimensional pair. Our main result gives an answer in the case R a and T a are quasilocal for each a.