Semigroup identities of tropical matrix semigroups of maximal rank

Zur Izhakian*

*Corresponding author for this work

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume92
Issue number3
Early online date30 Nov 2015
DOIs
Publication statusPublished - 1 Jun 2016

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Matrix Semigroups
Maximal Rank
Semigroup
Monoid
Triangular
Generalise

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Semigroup identities of tropical matrix semigroups of maximal rank. / Izhakian, Zur.

In: Semigroup Forum, Vol. 92, No. 3, 01.06.2016, p. 712-732.

Research output: Contribution to journalArticle

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KW - Semigroup representations

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