In this paper, we investigate the transfer of the properties of P-Bezout rings and 2-Bezout rings to the amalgamation of A and B along J with respect to f (denoted by A ⋈f J). Our aim is to provide necessary and sufficient conditions for A ⋈f J, to be a P-Bezout rings and 2-Bezout rings.

Let f : A → B be a ring homomorphism and J be an ideal of B. In this note, we investigate the transfer of the weak McCoy property to the amalgamation of A with B along J with respect to f (denoted by A⋈fJ) introduced and studied by D’Anna, Finocchiaro and Fontana in 2009. Our aim is to provide conditions under which A⋈fJ is a left weak McCoy (resp. right weak McCoy, McCoy) ring. Our results enrich the literature with new families of left weak McCoy (resp. right weak McCoy, weak McCoy) rings.

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