# On Pr\"ufer-like conditions

## TL;DR

This paper explores five extensions of Pr"ufer domains to rings with zero divisors, analyzing their stability under localization and homomorphic images, and providing new examples of such rings.

## Contribution

It introduces five new Pr"ufer-like conditions for rings with zero divisors and studies their stability, offering original examples and insights.

## Key findings

- Identified stability properties of Pr"ufer-like conditions under localization and homomorphic images.
- Generated new examples of rings satisfying these Pr"ufer-like conditions.
- Extended the concept of Pr"ufer domains to rings with zero divisors.

## Abstract

This paper deals with five extensions of the Pr\"ufer domain concept to commutative rings with zero divisors. We investigate the stability of these Pr\"ufer-like conditions under localization and homomorphic image. Our results generate new and original examples of Pr\"ufer-like rings.