Tensor products of higher almost split sequences in subcategories

We introduce the algebras satisfying the ( ℬ , n) condition. If Λ, Γ are algebras satisfying the ( ℬ , n ), ( ℰ , m ) condition, respectively, we give a construction of ( m + n )-almost split sequences in some subcategories ( B ⊗ E ) ( i 0 , j 0 ) of mod(Λ ⊗ Γ) by tensor products and mapping cones....

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Bibliographic Details
Published in:Czechoslovak mathematical journal 2023-12, Vol.73 (4), p.1151-1174
Main Authors: Lu, Xiaojian, Luo, Deren
Format: Article
Language:English
Subjects:
Algebra
Analysis
Convex and Discrete Geometry
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Tensors
Online Access:Get full text
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Summary:We introduce the algebras satisfying the ( ℬ , n) condition. If Λ, Γ are algebras satisfying the ( ℬ , n ), ( ℰ , m ) condition, respectively, we give a construction of ( m + n )-almost split sequences in some subcategories ( B ⊗ 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 ( ( B ⊗ E ) ( i 0 , j 0 ) , n + m ) condition for some integers i 0 , j 0 ; this construction unifies and extends the work of A. Pasquali (2017), (2019).
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2023.0432-22