Bi-amalgamated algebras along ideals

Let f: A → B and g: A → C be two commutative ring homomorphisms, and let J and J' be two ideals of B and C, respectively, such that f^-1(J) = g^-1(J'). The bi-amalgamation of A with (B, C) along (J, J') with respect to (f, g) is the subring of B×C given by A (bowtie)f;g (J, J ') := ( (f(a)+j, g(a)+j ') j a ∈ A, (J, J ') ∈ J×J '). In this paper, we investigate ring-theoretic properties of bi-amalgamations and capitalize on previous work carried out on various settings of pullbacks and amalgamations. In the second and third sections, we provide examples of bi- amalgamations and show how these constructions arise as pullbacks. The fourth section investigates the transfer of some basic ring theoretic properties to bi-amalgamations, and the fifth section is devoted to the prime ideal structure of these constructions. All new results agree with re- cent studies in the literature on D'Anna, Finocchiaro and Fontana's amalgamations and duplications.