Semigroup identities of tropical matrices through matrix ranks
Zur Izhakian, Glenn Merlet · arXiv (Cornell University) · 2018
We prove the conjecture that, for any $n$, the monoid of all $n \times n$ tropical matrices satisfies nontrivial semigroup identities. To this end, we prove that the factor rank of a large enough power of a tropical matrix does not exceed the tropical rank of the original matrix.