(Generalized) filter properties of the amalgamated algebra

Let $R$ and $S$ be commutative rings with unity, $f\colon R\rightarrow S$ a ring homomorphism $J$ an ideal of $S$. Then the subring $R\bowtie ^fJ:=\lbrace (a,f(a)+j)\mid a\in R$ $j\in J\rbrace $ $R\times is called amalgamation along respect to $f$. In this paper, we determine when ^fJ$ (generalized) filter ring.