Semigroup identities of supertropical matrices

Zur Izhakian, Glenn Merlet

Research output: Contribution to journalArticlepeer-review


We prove that, for any n, the monoid of all n× n supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities; in particular, such supertropical triangular matrices admit exactly the same identities satisfied by tropical triangular matrices. These semigroup identities are carried over to labeled-weighted digraphs with double arcs.

Original languageEnglish
Pages (from-to)466-477
Number of pages12
JournalSemigroup Forum
Issue number2
StatePublished - Oct 2022


  • Idempotent semirings
  • Semigroup identities
  • Semigroup representations
  • Supertropical matrices
  • Tropical (max-plus) matrices
  • Weighted diagraphs


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