Idempotent Ideals and the Igusa-Todorov Functions

Let Λ be an artin algebra and \(\mathfrak {A}\) a two-sided idempotent ideal of Λ, that is, \(\mathfrak {A}\) is the trace of a projective Λ-module P in Λ. We consider the categories of finitely generated modules over the associated rings \({\Lambda }/\mathfrak {A}, {\Lambda }\) and Γ = End_Λ(P) ^{o p} and study the relationship between their homological properties via the Igusa-Todorov functions.