Universally catenarian domains of 𝐷+𝑀 type

Abstract

Let T T be a domain of the form K + M K + M , where K K is a field and M M is a maximal ideal of T T . Let D D be a subring of K K and let R = D + M R = D + M . It is proved that if K K is algebraic over D D and both D D and T T are universally catenarian, then R R is universally catenarian. The converse holds if K K is the quotient field of D D . As a consequence, we construct for each n > 2 n > 2 , an n n -dimensional universally catenarian domain which does not belong to any previously known class of universally catenarian domains.