A note on strong locally divided domains

Abstract

A uniform proof is given for the following five assertions. Let $R$ be an integral domain such each overring of $R$ is a pseudovaluation domain (resp., divided domain; resp., going-down domain; resp., locally pseudovaluation domain; resp., locally divided domain). Then $R/P$ has the same property, for each prime ideal $P$ of $R$. The assertion for pseudovaluation domains was proved recently by Okabe-Yoshida by other methods.