Let [Formula: see text] and [Formula: see text] be two commutative rings with unity, let [Formula: see text] be an ideal of [Formula: see text] and [Formula: see text] be a ring homomorphism. In this paper, we give a characterization for the amalgamated algebra [Formula: see text] to be a Nagata ring, a strong S-domain, and a catenarian. Also, we investigate the conditions that the ring of Hurwitz series over [Formula: see text] has a complete comaximal factorization.
Let [Formula: see text] be a ring homomorphism and let [Formula: see text] be an ideal of [Formula: see text]. In this paper, we investigate the transfer of the [Formula: see text]-property from a ring [Formula: see text] to his amalgamated algebra [Formula: see text]. Our aim is to give new and original families of [Formula: see text]-rings which are neither [Formula: see text]-rings ([Formula: see text]) nor [Formula: see text]-rings ([Formula: see text]), and examples of [Formula: see text]-rings which are neither [Formula: see text]-rings ([Formula: see text]) nor [Formula: see text]-rings ([Formula: see text]).