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arXiv · 1608.04649

Relative Igusa-Todorov functions and relative homological dimensions

Marcelo Lanzilotta·Octavio Mendoza
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Abstract

We develope the theory of the $\mathcal{E}$-relative Igusa-Todorov functions in an exact $ IT$-context $(\mathcal{C},\mathcal{E}).$ In the case when $\mathcal{C}=$mod$\, (\Lambda)$ is the category of finitely generated left $\Lambda$-modules, for an artin algebra $\Lambda,$ and $\mathcal{E}$ is the class of all exact sequences in $\mathcal{C},$ we recover the usual Igusa-Todorov functions. We use the setting of the exact structures and the Auslander-Solberg relative homological theory to generalise the original Igusa-Todorov's results. Furthermore, we introduce the $\mathcal{E}$-relative Igusa-Todorov dimension and also we obtain relationships with the relative global and relative finitistic dimensions and the Gorenstein homological dimensions.

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Marcelo Lanzilotta, Octavio Mendoza. 2016-08-16. Relative Igusa-Todorov functions and relative homological dimensions. https://arxiv.org/abs/1608.04649

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