Gaps for the Igusa-Todorov function
Abstract
For a finite dimensional algebra $A$ with $0 < \phi dim (A) = m < \infty$ we prove that there always exist modules $M$ and $N$ such that $\phi(M) = m-1$ and $\phi (N) = 1$. On the other hand, we see an example of an algebra that not every value between $1$ and its $\phi$-dimension is reached by the $\phi$ function. We call that values gaps and we prove that the algebras with gaps verifies the finitistic conjecture.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2018
- DOI:
- 10.48550/arXiv.1810.12112
- arXiv:
- arXiv:1810.12112
- Bibcode:
- 2018arXiv181012112B
- Keywords:
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- Mathematics - Representation Theory
- E-Print:
- arXiv admin note: substantial text overlap with arXiv:1707.04774