  Let $A$ and $B$ be commutative rings with unity, $f:A\to B$ a ring
homomorphism 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 the
amalgamation of $A$ with $B$ along $J$ with respect to $f$. In this paper, we
study the property of Cohen-Macaulay in the sense of ideals which was
introduced by Asgharzadeh and Tousi, a general notion of the usual
Cohen-Macaulay property (in the Noetherian case), on the ring $A\bowtie^fJ$.
Among other things, we obtain a generalization of the well-known result that
when the Nagata's idealization is Cohen-Macaulay.
