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Keywords:
completely regular semigroup; lattice; variety; $\cap $-subsemilattice
completely regular semigroup; lattice; variety; $\cap $-subsemilattice
Summary:
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.
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