Semigroup identities of tropical matrix semigroups of maximal rank

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We show that any semigroup of n-by-n tropical matrices whose elements all have rank n (i.e., a nonsingular semigroup) satisfies a class of nontrivial semigroup identities. These identities generalize the identities satisfied by the monoid of all n-by-n triangular tropical matrices.

Original languageEnglish
Pages (from-to)712-732
Number of pages21
JournalSemigroup Forum
Issue number3
StatePublished - 1 Jun 2016
Externally publishedYes


  • Nonsingular matrices
  • Rank-maximal semigroups
  • Semigroup identities
  • Semigroup representations
  • Semigroup varieties
  • Tropical (max-plus) matrix algebra


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