Abstract
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.
Highlights
This article is organized as follows: after the introduction and the preliminary section devoted to fixing the notation and recalling the basic facts needed in this work, section 3 is devoted to Igusa-Todorov function for path rings
In [11] it was proved that if A is of Ωn-finite representation type for some n φdim(A) and ψdim(A) are both finite
Our objective is to introduce some properties that will be used
Summary
The concept of Gorenstein projective module goes back to a work of Auslander and Bridger [1]. In this work it was introduced the G-dimension for finitely generated modules over a two-sided noetherian ring. Later was proved by Avramov, Martisinkovsky, and Rieten that if M is a finitely generated module, M is Gorenstein projective if and only if the G-dimension of M is zero ( [3, Theorem 4.2.6]). [5] A finitely generated A-module G is Gorenstein projective if there exist a exact sequence:. [8] An Artin algebra A is called n-Gorenstein if id(A) ≤ n and pd(DAop) ≤ n with n ∈ N, where D = Homk(·, k). /0 be an exact sequence with Pi projective, K is a Gorenstein projective A-module
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