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arXiv · 2211.16012

Minimal monoids generating varieties with complex subvariety lattices

Sergey V. Gusev
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Abstract

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.

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Sergey V. Gusev. 2023-02-14. Minimal monoids generating varieties with complex subvariety lattices. https://doi.org/10.1017/s0013091524000178

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