A special chain theorem in the set of intermediate rings

摘要

Let R subset of S be an extension of integral domains, and let R* be the integral closure of R in S. The main purpose of this paper is to study [R, S], the set of intermediate rings between R and S. As a main tool, we establish an explicit description of any intermediate ring in terms of localizations of R (or R*). This study effectively enables us to characterize the minimal extensions in [R, S]. We also prove a special chain theorem concerning the length of an arbitrary maximal chain in [R,S]