Pr\"ufer- like conditions in the amalgamated duplication of a ring along an ideal

TL;DR

This paper explores five extensions of Pr"ufer domain properties to rings with zero-divisors, analyzing their transfer to the amalgamated duplication of a ring along an ideal, and introduces new classes of rings with these properties.

Contribution

It introduces five Pr"ufer-like conditions for rings with zero-divisors and studies their transfer to the amalgamated duplication, creating new classes of such rings.

Findings

Transfer of Pr"ufer-like properties between rings and their duplications

Identification of new classes of rings with Pr"ufer-like properties

Extension of Pr"ufer domain concepts to rings with zero-divisors

Abstract

In this paper, we consider five possible extensions of the Pr\"ufer domain notion to the case of commutative rings with zero-divisors. We investigate the transfer of these Pr\"ufer-like properties between a ring $R$ and $R\bowtie I$; his amalgamated duplication along some ideal $I$, and then generate new and original families of rings with these properties.