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Relative Igusa-Todorov Functions and Relative Homological Dimensions

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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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Authors and Affiliations

  1. Instituto de Matemática y Estadística “Rafael Laguardia”, J. Herrera y Reissig 565, Facultad de Ingeniería, Universidad de la República., CP, 11300, Montevideo, Uruguay

    Marcelo Lanzilotta

  2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad de México, México

    Octavio Mendoza

  3. Circuito Exterior, Ciudad Universitaria, CP, 04510, Ciudad de México, México

    Octavio Mendoza

Authors
  1. Marcelo Lanzilotta
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  2. Octavio Mendoza
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Correspondence to Octavio Mendoza.

Additional information

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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