n-coherence property in amalgamated algebra along an ideal

Abstract

Let  $f: A\rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. The purpose of this article is to examine the transfer of the properties of $n$-coherence and strong $n$-coherence $(n\geq 2)$ from a ring $A$ to his amalgamated algebra $A\bowtie^{f} J$. Our results generate examples which enrich the current literature with new and original families of $n$-coherent rings that are not $(n-1)$-coherent rings.