# Semigroup identities of tropical matrices through matrix ranks

Zur Izhakian, Glenn Merlet

Research output: Working paper

### Abstract

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.
Original language English ArXiv Submitted - 28 Jun 2018

### Keywords

• math.RA
• math.CO
• 20M05, 20M07, 20M30, 47D03