2009/02/08 by Zur Izhakian, Izhakian, Zur, Stuart Margolis +1
Computer Science · Mathematics · #16Y60 #20M07 #Coding theory and cryptography #FOS: Mathematics #Group Theory (math.GR) #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.GR #math.RA #msc:16Y60 #msc:20M07 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0902.1174
arxiv created 2009/02/08 · openalex publication_date 2009/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result of the paper proves that the monoid of all 2 x 2 tropical matrices satisfies a non-trivial semigroup identity, unlike the case of matrices over infinite fields. We exploit a strong connection between the monoid of all 2 x 2 tropical matrices and the bicyclic monoid to show that a variant of Adian's identity for the bicyclic monoid holds in our case.We use generic matrices of tropical polynomials to prove our result.