Tropical one-relation monoids

2022/09/26 by Carl‐Fredrik Nyberg‐Brodda, Nyberg-Brodda, Carl-Fredrik
Computer Science · #20F05 (secondary) #20M05 (primary) 15A80 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2209.12612

openalex publication_date 2022/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2010, Izhakian & Margolis proved that the bicyclic monoid admits a representation as a semigroup of upper triangular tropical matrices. We extend this result by classifying all one-relation monoids which admit such representations. We also classify, with two exceptions, all one-relation monoids which admit representations as semigroups of tropical matrices.

Related

• Semigroup identities in the monoid of two-by-two tropical matrices
• Tropical linear representations of the Chinese monoid
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• Semigroup identities of tropical matrices through matrix ranks
• Semigroup identities in the monoid of triangular tropical matrices