Semigroup identities of tropical matrices through matrix ranks

Zur Izhakian, Glenn Merlet

Research output: Working paper

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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 languageEnglish
Publication statusSubmitted - 28 Jun 2018

Bibliographical note

13 pages


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


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