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On residually integrally closed domains

Echi O., Jarboui N.

Demonstratio Mathematica

2003

Vol. 36, nr 3

543--550

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