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 $Λ/\mathfrak{A}, Λ$ and $Γ=\mathrm{End}_Λ(P)^{op}$ and study the relationship between their homological properties via the Igusa-Todorov functions.

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