Abstract
We develope the theory of \({\mathcal {E}}\)-relative Igusa-Todorov functions in an exact I T-context \(({\mathcal {C}},{\mathcal {E}})\) (see Definition 2.1). In the case when \({\mathcal {C}}={\text {mod}}\, ({\Lambda })\) is the category of finitely generated left Λ-modules, for an artin algebra Λ, and \({\mathcal {E}}\) is the class of all exact sequences in \({\mathcal {C}},\) we recover the usual Igusa-Todorov functions, Igusa K. and Todorov G. (2005). 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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Presented by Henning Krause.
We dedicate this paper to Eduardo Marcos on his sixtieth birthday
The authors thanks the Project PAPIIT-Universidad Nacional Autónoma de México IN102914. This work has been partially supported by project MathAmSud-RepHomol.
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Lanzilotta, M., Mendoza, O. Relative Igusa-Todorov Functions and Relative Homological Dimensions. Algebr Represent Theor 20, 765–802 (2017). https://doi.org/10.1007/s10468-016-9664-x
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DOI: https://doi.org/10.1007/s10468-016-9664-x