E-viri
Recenzirano
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Ma, Xin; Peng, Ye Yang; Huang, Zhao Yong
Acta mathematica Sinica. English series, 04/2024, Letnik: 40, Številka: 4Journal Article
We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements. Let Λ′, Λ, Λ″ be artin algebras such that (mod Λ′, mod Λ, mod Λ′) is a recollement, and let D ′ and D ′ ′ be subcategories of mod Λ′ and mod Λ″ respectively. For any n, m ≥ 0, under some conditions, we get dim Ω k ( D ) ≤ dim Ω n ( D ′ ) + dim Ω m ( D ′ ′ ) + 1 , where k = max{ m, n } and D is the subcategory of mod Λ glued by D ′ and D ′ ′ ; moreover, we give a sufficient condition such that the converse inequality holds true. As applications, some results for Igusa–Todorov subcategories and syzygy finite subcategories are obtained.
