Idempotent ideals and the Igusa-Todorov functions

Abstract

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