### 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 |
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Publisher | ArXiv |

Publication status | Submitted - 28 Jun 2018 |

### Keywords

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

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## Cite this

Izhakian, Z., & Merlet, G. (2018).

*Semigroup identities of tropical matrices through matrix ranks*. ArXiv. http://arxiv.org/abs/1806.11028v1