Bi-amalgamation of rings defined by certain annihilator conditions

Abstract

Let $f:A\to B$ and $g:A\to C$ be two ring homomorphisms and let $J$ (resp. $J^{\prime }$) be an ideal of $B$ (resp. $C$) such that $f^{-1}\left(J\right)=g^{-1}\left(J^{\prime }\right)$. We investigate the transfer of the notions of (A)-rings and strong (A)-rings to the bi-amalgamation of $A$ with $\left(B,C\right)$ along $\left(J,J^{\prime }\right)$ with respect to $\left(f,g\right)$, denoted by $A{\bowtie }^{f,g}\left(J,J^{\prime }\right)$, introduced and studied by Kabbaj, Louartiti and Tamekkante in 2013. Our results generate new original examples of rings satisfying these properties.