Mohammed Tamekkante, El Mehdi Bouba

Published:

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 by $ A\bowtie ^{f,g}(J,J^{\prime }) = \{(f(a)+j,g(a)+j^{\prime })/ a \in A, (j,j^{\prime }) \in J\times J^{\prime }\}. $ In this paper, we study the weak global dimension of coherent bi-amalgamations.AbstractLet 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 by $ A\bowtie ^{f,g}(J,J^{\prime }) = \{(f(a)+j,g(a)+j^{\prime })/ a \in A, (j,j^{\prime }) \in J\times J^{\prime }\}. $ In this paper, we study the weak global dimension of coherent bi-amalgamations.fABgACJJBCf−1Jg−1JABCJJfgBC $ A\bowtie ^{f,g}(J,J^{\prime }) = \{(f(a)+j,g(a)+j^{\prime })/ a \in A, (j,j^{\prime }) \in J\times J^{\prime }\}. $ $ A\bowtie ^{f,g}(J,J^{\prime }) = \{(f(a)+j,g(a)+j^{\prime })/ a \in A, (j,j^{\prime }) \in J\times J^{\prime }\}. $