Igusa-Todorov function on path rings
Résumé
The aim of this paper is to study the relation between the Igusa-Todorov functions for $A$, a finite dimensional algebra, and the algebra $AQ$. In particular it is proved that $\fidim (AQ) = \fidim (A) + 1$ when $A$ is a Gorenstein algebra. As a consequence of the previous result, it is exhibited an example of a family of algebras $\{A_n\}_{n \in \mathbb{N}}$ such that $\fidim (A_n) = n$ and each $A_n$ is of $\Omega^{\infty}$-infinite representation type.Téléchargements
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