Bi-amalgamated algebras along ideals

Abstract

Abstract. 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 thatThis paper investigates ring-theoretic properties of bi-amalgamations and capitalizes on previous works carried 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 recent studies in the literature on D'Anna-Finocchiaro-Fontana's amalgamations and duplications.

Global dimension of bi-amalgamated algebras along pure ideals

“…The aim of this paper is to give a preliminary study of the (weak) global dimension of a subclass of pullbacks rings called bi-amalgamated algebras introduced in [5].…”

“…In [5], the authors studied ring-theoretic properties of bi-amalgamations, provided examples of bi-amalgamations, studied the transfer of some basic ring theoretic properties to bi-amalgamations and described the prime ideal structure of these constructions. They also showed how these constructions arise as pullbacks.…”

Bi-Amalgamation of Small Weak Global Dimension

“…The aim of this paper is to study the weak global dimension of a subclass of pullbacks rings called bi-amalgamated algebras introduced in [13].…”

“…This construction was introduced in [13] as a natural generalization of duplications [5,6] and amalgamations [7,8]. Given a ring homomorphism f : A → B and an ideal …”

“…In [13], the authors provide original examples of bi-amalgamations and, in particular, show that Boisen-Sheldon's CPI-extensions [3] can be viewed as bi-amalgamations. They also showed how these bi-amalgamations arise as pullbacks.…”