A special chain theorem in the set of intermediate rings.

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