2023/10/12 by Thomas Aird, Aird, Thomas, Duarte Ribeiro +1 · 1 citation
Mathematics · Computer Science · #Rings, Modules, and Algebras #Advanced Algebra and Logic #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2310.08682
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.