2014/07/26 by S. Kabbaj, Kabbaj, S., K. Louartit +3
Mathematics · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1407.7074
openalex publication_date 2014/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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\bowtief,g(J,J'):=\(f(a)+j,g(a)+j') | a∈ A, (j,j')∈ J× J'\. This 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.