Semigroup identities in the monoid of two-by-two tropical matrices

Zur Izhakian, Stuart W. Margolis

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

We show that the monoid of 2×2 tropical matrices is a regular semigroup satisfying the semigroup identity Studying reduced identities for subsemigroups of and introducing a faithful semigroup representation for the bicyclic monoid by 2×2 tropical matrices, we reprove Adjan's identity for the bicyclic monoid in a much simpler way.

Original languageEnglish
Pages (from-to)191-218
Number of pages28
JournalSemigroup Forum
Volume80
Issue number2
DOIs
StatePublished - 2010
Externally publishedYes

Keywords

  • Idempotent semiring
  • Monoid representation
  • Regular monoids
  • Semigroup identity
  • Tropical (max-plus) matrix algebra

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