Semigroup identities in the monoid of triangular tropical matrices

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8 Citations (Scopus)

Abstract

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
Volume88
Issue number1
Early online date22 Jun 2013
DOIs
Publication statusPublished - Feb 2014

Keywords

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

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