Global dimension of bi-amalgamated algebras along pure ideals

Abstract

Let f : A → B and g : A → C be two 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 byThe aim of this paper is to characterize the global dimension of bi-amalgamated algebras over pure ideals.

Bi-Amalgamation of Small Weak Global Dimension

“…In this paper, we characterize the bi-amalgamations of small weak global dimension. All obtained results recover and compare to previous works carried on various settings of duplications and amalgamations, and capitalize on recent results on bi-amalgamations ( [1,4,14,18]).…”