On residually integrally closed domains

A domain R is called residually integrally closed if R/p is an integrally closed domain for each prime ideal p of R. We show that residually integrally closed domains satisfy some chain conditions on prime ideals. We give characterization of such domains in case they contain a field of characteristic 0. Section 3 deals with domains R such that R/p is a unique factorization domain for each prime ideal p of R, these domains are showed to be PID. We also prove that domains R such that R/p is a regular domain are exactly Dedekind domains.