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Coherence in Bi-amalgamated Algebras Along Ideals

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Homological and Combinatorial Methods in Algebra (SAA 2016)

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Abstract

Let \(f: A\longrightarrow B\) and \(g: A\longrightarrow C\) be two ring homomorphisms and let J (resp., \(J'\)) be an ideal of B (resp., C) such that \(f^{-1}(J)=g^{-1}(J')\). In this paper, we investigate the transfer of the property of coherence in the bi-amalgamation of A with (B, C) along \((J,J')\) with respect to (f, g) (denoted by \(A\bowtie ^{f,g}(J,J'))\), introduced and studied by Kabbaj, Louartiti, and Tamekkante in 2013. We provide necessary and sufficient conditions for \(A\bowtie ^{f,g}(J,J')\) to be a coherent ring.

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Acknowledgment

The authors would like to express their sincere thanks to the referee for his/her helpful suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology of Fez, University S. M. Ben Abdellah Fez, Box 2202, Fes, Morocco

    Mounir El Ouarrachi & Najib Mahdou

Authors
  1. Mounir El Ouarrachi
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  2. Najib Mahdou
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Corresponding author

Correspondence to Najib Mahdou .

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Editors and Affiliations

  1. Department of Mathematics, American University of Sharjah, Sharjah, United Arab Emirates

    Ayman Badawi

  2. Faculty of Mathematical Science, Isfahan University of Technology, Isfahan, Iran

    Mohammad Reza Vedadi

  3. School of Mathematics, Statistics, and Computer Science, University of Tehran, Tehran, Iran

    Siamak Yassemi

  4. Department of Mathematics and Applications, University of Mohaghegh Ardabili, Ardabil, Iran

    Ahmad Yousefian Darani

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Ouarrachi, M.E., Mahdou, N. (2018). Coherence in Bi-amalgamated Algebras Along Ideals. In: Badawi, A., Vedadi, M., Yassemi, S., Yousefian Darani, A. (eds) Homological and Combinatorial Methods in Algebra. SAA 2016. Springer Proceedings in Mathematics & Statistics, vol 228. Springer, Cham. https://doi.org/10.1007/978-3-319-74195-6_13

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