Gaps for the Igusa-Todorov function

Abstract

For a finite dimensional algebra $A$ with $0<\varphi dim(A)=m<\infty$ we prove that there always exist modules $M$ and $N$ such that $\varphi (M)=m-1$ and $\varphi (N)=1$. On the other hand, we see an example of an algebra that not every value between $1$ and its $\varphi$-dimension is reached by the $\varphi$ function. We call that values gaps and we prove that the algebras with gaps verifies the finitistic conjecture.

arXiv admin note: substantial text overlap with arXiv:1707.04774