Geodesic
Relations on a lattice of varieties of completely regular semigroups
Mathematica Bohemica, Tome 145 (2020) no. 3, pp. 225-240 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $.
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 $.
DOI : 10.21136/MB.2019.0050-18
Classification : 20M07
Keywords: semigroup; completely regular; variety; lattice; relation; kernel; trace; local relation; core 
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Petrich, Mario. Relations on a lattice of varieties of completely regular semigroups. Mathematica Bohemica, Tome 145 (2020) no. 3, pp. 225-240. doi: 10.21136/MB.2019.0050-18

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