Igusa-Todorov functions for Artin algebras

In this paper we study the behaviour of the Igusa-Todorov functions for Artin algebras A with finite injective dimension, and Gorenstein algebras as a particular case. We show that the $ϕ$-dimension and $ψ$-dimension are finite in both cases. Also we prove that monomial, gentle and cluster tilted algebras have finite $ϕ$-dimension and finite $ψ$-dimension.

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