Semigroup identities of tropical matrix semigroups of maximal rank

Zur Izhakian*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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
Early online date30 Nov 2015
Publication statusPublished - 1 Jun 2016

Bibliographical note


The author would like to thank the referee for his comments and helpful suggestions.


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


Dive into the research topics of 'Semigroup identities of tropical matrix semigroups of maximal rank'. Together they form a unique fingerprint.

Cite this