Finite conductor property in amalgamated algebra along an ideal

Let f : A → B be a ring homomorphism, J be an ideal of B. In this paper, we investigate the finite conductor property that the amalgamation A ⋈ fJ might inherit from the ring A for some classes of ideals J and homomorphisms f. Our results generate original examples which enrich the current literature with new families of examples of non-coherent finite conductor rings.