Idempotent ideals and the Igusa-Todorov functions

TL;DR

This paper investigates the homological properties of modules over certain algebraic structures related to artin algebras, using Igusa-Todorov functions to understand the impact of idempotent ideals.

Contribution

It introduces a new framework connecting homological properties of modules over artin algebras with idempotent ideals via Igusa-Todorov functions.

Findings

Established relationships between homological properties of modules over different associated rings.

Provided new insights into the structure of modules over artin algebras with idempotent ideals.

Extended the application of Igusa-Todorov functions in homological algebra.

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.