Universally catenarian integral domains

Abstract

The rings of the title are the (not necessarily Noetherian) integral domains R such that R[ X 1, …, X n ] is catenarian for each positive integer n. It is proved that each such R must be a stably strong S-domain, in the sense of Malik-Mott. The class of all universally catenarian integral domains is characterized as the largest class of catenarian integral domains which is stable under factor domains and localizations and whose members R satisfy the altitude formula and dim V ( R) = dim( R). Moreover, the following theorem is given, generalizing Ratliff's result that each one-dimensional Noetherian integral domain is universally catenarian. Let R be a locally finite-dimensional going-down domain; then R is universally catenarian if and only if the integral closure of R is a Prüfer domain. Other results and applications are also given.