Universally catenarian domains ofD+Mtype, II

[摘要] LetTbe a domain of the formK+M, whereKis a field andMis a maximal idealofT. LetDbe a subring ofKsuch thatR=D+Mis universally catenarian. ThenDisuniversally catenarian andKis algebraic overk, the quotient field ofD. If[K:k]<∞, thenTisuniversally catenarian. Consequently,Tis universally catenarian ifRis either Noetherian or agoing-down domain. A key tool establishes that universally going-between holds for any domainwhich is module-finite over a universally catenarian domain.

[学科分类] 数学（综合）