Igusa–Todorov functions for Artin algebras.

In this paper we study the behavior 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. [ABSTRACT FROM AUTHOR]