Identities of tropical matrix semigroups and the plactic monoid of rank 4
| Autor: | Thomas Aird |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | International Journal of Algebra and Computation. 32:1083-1100 |
| ISSN: | 1793-6500 0218-1967 |
| DOI: | 10.1142/s0218196722500461 |
| Popis: | We study semigroup varieties generated by full and upper triangular tropical matrix semigroups and the plactic monoid of rank 4. We prove that the upper triangular tropical matrix semigroup [Formula: see text] generates a different semigroup variety for each dimension [Formula: see text]. We show a weaker version of this fact for the full matrix semigroup: full tropical matrix semigroups of different prime dimensions generate different semigroup varieties. For the plactic monoid of rank 4, [Formula: see text], we find a new set of identities satisfied by [Formula: see text] shorter than those previously known, and show that the semigroup variety generated by [Formula: see text] is strictly contained in the variety generated by [Formula: see text]. |
| Databáze: | OpenAIRE |
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