Igusa-Todorov functions for Artin algebras

Abstract

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 $\varphi$-dimension and $\psi$-dimension are finite in both cases. Also we prove that monomial, gentle and cluster tilted algebras have finite $\varphi$-dimension and finite $\psi$-dimension.