Let $ R $ be an Artin algebra, $ \mathrm{mod}R $ be the category of finitely generated right $ R $-modules, and let $ F $ be a sub-bifunctor of $ \mathrm{Ext}^{1}_{R}(-, -) $. In this paper, we introduce the notion of the $ F $-extension dimension for $ \mathrm{mod}R $. We further establish the relationships for the finiteness among the $ F $-extension dimension, $ F $-finitistic dimension and $ F $-Igusa-Todorov dimension.
Citation: Pei Luo, Junjie Zhang. The finiteness of relative homological dimensions[J]. Electronic Research Archive, 2026, 34(7): 4648-4660. doi: 10.3934/era.2026205
Let $ R $ be an Artin algebra, $ \mathrm{mod}R $ be the category of finitely generated right $ R $-modules, and let $ F $ be a sub-bifunctor of $ \mathrm{Ext}^{1}_{R}(-, -) $. In this paper, we introduce the notion of the $ F $-extension dimension for $ \mathrm{mod}R $. We further establish the relationships for the finiteness among the $ F $-extension dimension, $ F $-finitistic dimension and $ F $-Igusa-Todorov dimension.
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Pei Luo, Junjie Zhang. The finiteness of relative homological dimensions[J]. Electronic Research Archive, 2026, 34(7): 4648-4660. doi: 10.3934/era.2026205
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