Gaussian and Prüfer conditions in bi-amalgamated algebras

Abstract

Let f : A → B and g : A → C be two ring homomorphisms and let J (resp., J ′ ) be an ideal of B (resp., C) such that f −1 (J) = g −1 (J ′ ). In this paper, we investigate the transfer of the notions of Gaussian and Prüfer properties to the bi-amalgamation of A with (B, C) along (J, J ′ ) with respect to ( f, g) (denoted by A ⊲⊳ f ,g (J, J ′ )), introduced and studied by Kabbaj, Louartiti and Tamekkante in 2013. Our results recover well known results on amalgamations in [15] and generate new original examples of rings satisfying these properties.