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A semilattice of varieties of completely regular semigroups
Mathematica Bohemica, Tome 145 (2020) no. 1, pp. 1-14
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Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by $\mathcal L(\mathcal C\mathcal R)$. \endgraf We construct a 60-element $\cap $-subsemilattice and a 38-element sublattice of $\mathcal L(\mathcal C\mathcal R)$. The bulk of the paper consists in establishing the necessary joins for which it uses Polák's theorem.
Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by $\mathcal L(\mathcal C\mathcal R)$. \endgraf We construct a 60-element $\cap $-subsemilattice and a 38-element sublattice of $\mathcal L(\mathcal C\mathcal R)$. The bulk of the paper consists in establishing the necessary joins for which it uses Polák's theorem.
DOI : 10.21136/MB.2018.0112-17
Classification : 20M07
Keywords: completely regular semigroup; lattice; variety; $\cap $-subsemilattice 
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Petrich, Mario. A semilattice of varieties of completely regular semigroups. Mathematica Bohemica, Tome 145 (2020) no. 1, pp. 1-14. doi: 10.21136/MB.2018.0112-17

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