n-Coherence and (n, d)- properties in amalgamated algebra

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 from a ring $A$ to his amalgamated algebra $A\bowtie^{f} J$. Also, we investigate the $(n,d)$-property of the amalgamated algebra $A \bowtie^{f}J$, to resolve Costa's first conjecture.

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