Pr\"ufer-like conditions on an amalgamated algebra along an ideal

TL;DR

This paper investigates Pr"ufer-like conditions within a specific ring construction called amalgamation along an ideal, extending the understanding of these conditions in algebraic structures.

Contribution

It introduces new insights into Pr"ufer-like conditions in amalgamated algebras along an ideal, building upon the construction introduced by D'Anna, Finocchiaro, and Fontana.

Findings

Characterization of Pr"ufer-like conditions in amalgamated algebras

Extension of classical Pr"ufer conditions to new algebraic contexts

Identification of conditions under which amalgamation preserves Pr"ufer-like properties

Abstract

Let $f:A\longrightarrow B$ be a ring homomorphism and let $\mathfrak b$ be an ideal of $B$. In this paper we study Pr\"ufer like conditions in the amalgamation of $A$ with $B$ along $\mathfrak b$, with respect to $f$, a ring construction introduced in 2009 by D'Anna, Finocchiaro and Fontana.