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1 results

  • Minimal monoids generating varieties with complex subvariety lattices

  • Part of
  • Sergey V. Gusev
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 67 / Issue 2 / May 2024
    Published online by Cambridge University Press:
    22 March 2024, pp. 617-642
    • Article
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  • A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. We show that the 6-element Brandt monoid generates a finitely universal variety of monoids and, by the previous results, it is the smallest generator for a monoid variety with this property. It is also deduced that the join of two Cross varieties of monoids can be finitely universal. In particular, we exhibit a finitely universal variety of monoids with uncountably many subvarieties which is the join of two Cross varieties of monoids whose lattices of subvarieties are the 6-element and the 7-element chains, respectively.