Semigroup identities in the monoid of triangular tropical matrices

Zur Izhakian

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


We show that the submonoid of all n×n triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities. The utilization of the Fibonacci number formula gives us an upper bound on the length of these 2-variable semigroup identities.
Original languageEnglish
Pages (from-to)145-161
Number of pages17
JournalSemigroup Forum
Issue number1
Early online date22 Jun 2013
Publication statusPublished - Feb 2014

Bibliographical note

The author thanks Glenn Merlet for the useful conversation in CIRM, Luminy, September 2011. The author would like to thank the referee for many valuable comments and helpful suggestions.


  • Tropical (max-plus) matrix algebra
  • Idempotent semirings
  • Semigroup identities
  • Semigroup varieties
  • Monoid representations


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