Semigroup identities of tropical matrices through matrix ranks

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.

13 pages

References in corpus (2)

• Identities in Upper Triangular Tropical Matrix Semigroups and the Bicyclic Monoid
• Remarks on separating words

Cited by in corpus (1)

• Identities of tropical matrices and plactic monoids