Abstract
We introduce the algebras satisfying the (\({\cal B}\), n) condition. If Λ, Γ are algebras satisfying the (\({\cal B}\), n), (\({\cal E}\), m) condition, respectively, we give a construction of (m+n)-almost split sequences in some subcategories \({({\cal B} \otimes {\cal E})^{({i_0},{j_0})}}\) of mod(Λ ⊗ Γ) by tensor products and mapping cones. Moreover, we prove that the tensor product algebra Λ ⊗ Γ satisfies the \(({({\cal B} \otimes {\cal E})^{({i_0},{j_0})}},n + m)\) condition for some integers i0, j0; this construction unifies and extends the work of A. Pasquali (2017), (2019).
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The research has been supported by the National Natural Science Foundation of China under Grants #11901191 and #12071120, the Scientific Research Foundation of Hunan Provincial Education Department (CN) #21B0599, the research and innovation team of Hunan Institute of Science and Technology #2019-TD-15 and the Construct Program of the Key Discipline in Hunan Province.
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Lu, X., Luo, D. Tensor products of higher almost split sequences in subcategories. Czech Math J 73, 1151–1174 (2023). https://doi.org/10.21136/CMJ.2023.0432-22
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DOI: https://doi.org/10.21136/CMJ.2023.0432-22