A note on maximal non-Noetherian subrings of a domain

This paper is concerned with the prime spectrum of maximal non-Noetherian subrings of a given domain. It is proved that if R is a maximal non-Noetherian subring of S, then R is a stably strong S-domain and that R is universally catenarian iff S is universally catenarian. Our main results lead to new examples of stably strong S-domains and universally catenarian domains. The relationship with n-dimensional pairs and residually Mori pairs is established.