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# Article

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Keywords:
semigroup; completely regular; variety; lattice; relation; kernel; trace; local relation; core
Summary:
Completely regular semigroups $\mathcal {CR}$ are considered here with the unary operation of inversion within the maximal subgroups of the semigroup. This makes $\mathcal {CR}$ a variety; its lattice of subvarieties is denoted by $\mathcal {L(CR)}$. We study here the relations ${\mathbf K,T,L}$ and ${\mathbf C}$ relative to a sublattice $\Psi$ of $\mathcal {L(CR)}$ constructed in a previous publication. \endgraf For ${\mathbf R}$ being any of these relations, we determine the ${\mathbf R}$-classes of all varieties in the lattice $\Psi$ as well as the restrictions of ${\mathbf R}$ to $\Psi$.
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