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Semigroup identities of tropical matrices through matrix ranks
Published 28 Jun 2018 in math.RA and math.CO | (1806.11028v1)
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.
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