Lattices of varieties of plactic-like monoids
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916106250223616 |
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| author | Aird, Thomas Ribeiro, Duarte |
| author_facet | Aird, Thomas Ribeiro, Duarte |
| contents | We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the axiomatic ranks of their elements, obtain plactic-like congruences whose corresponding factor monoids generate varieties in the lattice, and determine which varieties are joins of the variety of commutative monoids and a finitely generated variety. We also show that the hyposylvester and metasylvester monoids generate the same variety as the sylvester monoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08682 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lattices of varieties of plactic-like monoids Aird, Thomas Ribeiro, Duarte Rings and Algebras Combinatorics 20M07 (Primary) 05E16, 08B05, 08B15, 20M05 (Secondary) We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the axiomatic ranks of their elements, obtain plactic-like congruences whose corresponding factor monoids generate varieties in the lattice, and determine which varieties are joins of the variety of commutative monoids and a finitely generated variety. We also show that the hyposylvester and metasylvester monoids generate the same variety as the sylvester monoid. |
| title | Lattices of varieties of plactic-like monoids |
| topic | Rings and Algebras Combinatorics 20M07 (Primary) 05E16, 08B05, 08B15, 20M05 (Secondary) |
| url | https://arxiv.org/abs/2310.08682 |