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Let $A$ and $B$ be commutative rings with unity, $f:A\to B$ a ringhomomorphism and $J$ an ideal of $B$. Then the subring$A\bowtie^fJ:=\{(a,f(a)+j)|a\in A$ and $j\in J\}$ of $A\times B$ is called theamalgamation of $A$ with $B$ along with $J$ with respect to $f$. In this paper,among other things, we investigate the Cohen-Macaulay and (quasi-)Gorensteinproperties on the ring $A\bowtie^fJ$.

Cohen-Macaulay and Gorenstein properties under the amalgamated construction