Universally catenarian domains of D+M type, II

Abstract

Let T be a domain of the form K+M, where K is a field and M is a maximal ideal of T. Let D be a subring of K such that R=D+M is universally catenarian. Then D is universally catenarian and K is algebraic over k, the quotient field of D. If [K:k]<∞, then T is universally catenarian. Consequently, T is universally catenarian if R is either Noetherian or a going-down domain. A key tool establishes that universally going-between holds for any domain which is module-finite over a universally catenarian domain.

Keywords

• universally catenarian
• going between
• altitude formula.