The finiteness of relative homological dimensions

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Abstract

Let R be an Artin algebra, modR be the category of finitely generated rightR- modules, and letF be a sub-bifunctor of $\operatorname{Ext}_{R}^{1}(-,-)$. In this paper, we introduce the notion of the F-extension dimension for modR. We further establish the relationships for the finiteness among the F-extension dimension,F-finitistic dimension andF-Igusa-Todorov dimension.

Keywords

relative extension dimension / relative finitistic dimension / relative Igusa-Todorov dimension

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