ON MAXIMAL NON-UNIVERSALLY CATENARIAN SUBRINGS

Abstract

An integral domain R with field of fractions K is called a maximal non-1-catenarian subring of K if the polynomial ring in one variable, R[X] is not catenarian and for each proper intermediate ring T (that is each ring T such that R ⊂ T ⊆ K) T[X] is catenarian. The main purpose of this paper is to prove that the concept of maximal non-1-catenarian subrings and that of maximal non-universally catenarian subrings are equivalent.