Quasi-Prufer extensions of rings

TL;DR

This paper introduces quasi-Prufer and almost-Prufer ring extensions, providing characterizations and exploring their properties and relationships with the finite fibers property, to generalize and contextualize existing notions in ring theory.

Contribution

It defines and studies quasi-Prufer and almost-Prufer extensions, extending the concept of quasi-Prufer domains to broader ring extension contexts.

Findings

Characterizations of quasi-Prufer extensions

Properties of almost-Prufer extensions

Relationship with the finite fibers property

Abstract

We introduce quasi-Prufer extensions of rings in order to relativize the notion of quasi-Prufer domains and to take into account some contexts recently introduced in the literature. We also introduce almost-Prufer ring extensions. Characterizations and properties are given. In particular, we examine the relationship with the finite fibers property.