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Note on the Weak Global Dimension of Coherent Bi-amalgamations

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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.

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Acknowledgments

The authors would like to express their sincere thanks to the referee for his/her careful reading of the manuscript and several useful comments, which have greatly improved this article.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University Moulay Ismail Meknes, Box 11201, Zitoune, Morocco

    Mohammed Tamekkante & El Mehdi Bouba

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  1. Mohammed Tamekkante
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  2. El Mehdi Bouba
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Correspondence to Mohammed Tamekkante.

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Tamekkante, M., Bouba, E.M. Note on the Weak Global Dimension of Coherent Bi-amalgamations. Vietnam J. Math. 45, 639–649 (2017). https://doi.org/10.1007/s10013-016-0236-5

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  • DOI: https://doi.org/10.1007/s10013-016-0236-5

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