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

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dc.creatorIzhakian, Zur
dc.creatorMargolis, Stuart
dc.date2009-02-08
dc.date.accessioned2026-07-07T12:39:17Z
dc.date.available2026-07-07T12:39:17Z
dc.descriptionThe 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.
dc.identifierhttps://arxiv.org/abs/0902.1174
dc.identifierhttp://arxiv.org/abs/0902.1174
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219056
dc.subjectGroup Theory
dc.subjectRings and Algebras
dc.subject20M07, 16Y60
dc.titleSemigroup identities in the monoid of two-by-two tropical matrices
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