On quasi-Pr\"{u}fer and UM$t$ domains

TL;DR

This paper characterizes quasi-Prüfer and UM$t$ domains through properties of overrings and introduces new characterizations for these classes of integral domains.

Contribution

It provides novel equivalences for quasi-Prüfer domains involving $w$-Jaffard, $w$-stably strong S, and $w$-strong S domains, along with new characterizations of UM$t$ domains.

Findings

Quasi-Prüfer domains are characterized by all overrings being $w$-Jaffard domains.

Alternative characterizations involve $w$-stably strong S and $w$-strong S domains.

New criteria for UM$t$ domains are established.

Abstract

In this note we show that an integral domain $D$ of finite $w$-dimension is a quasi-Pr\"{u}fer domain if and only if each overring of $D$ is a $w$-Jaffard domain. Similar characterizations of quasi-Pr\"{u}fer domains are given by replacing $w$-Jaffard domain by $w$-stably strong S-domain, and $w$-strong S-domain. We also give new characterizations of UM$t$ domains.