Pr\"ufer conditions under the amalgamated construction

TL;DR

This paper investigates how Pr"ufer, Gaussian, and arithmetical properties transfer to amalgamated algebraic constructions, providing new results, answering open questions, and constructing examples.

Contribution

It improves recent transfer results for these properties in amalgamated constructions and addresses an open question in the field.

Findings

Enhanced transfer criteria for Pr"ufer, Gaussian, and arithmetical conditions

Answered a specific open question in the literature

Constructed examples illustrating the theoretical results

Abstract

In this paper we improve the recent results on the transfer of Pr\"ufer, Gaussian and arithmetical conditions on amalgamated constructions. As an application we provide an answer to a question posed by Chhiti, Jarrar, Kabbaj and Mahdou as well as we construct various examples.