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A conjecture for varieties of completely regular semigroups

In: Mathematica Slovaca, vol. 69, no. 3
Mario Petrich
Detaily:
Rok, strany: 2019, 541 - 556
Kľúčové slová:
semigroup, completely regular, relation, operation, variety, canonical
O článku:
The class $\mathscr{CR}$ of completely regular semigroups considered with the unary operation of inversion within maximal subgroups forms a variety. The $\mathbf{B}$-relation on the lattice $\mathscr{L}(\mathscr{CR})$ of subvarieties of $\mathscr{CR}$ identifies two varieties if they contain the same bands. Its classes are intervals with the set $Δ$ of upper ends of these intervals. Canonical varieties form part of $Δ$. Previously we determined the sublattice $Ψ$ of $\mathscr{L}(\mathscr{CR})$ generated by the variety $\mathscr{CS}$ of completely simple semigroups and six canonical varieties. The conjecture is that the sublattice of $\mathscr{L}(\mathscr{CR})$ generated by $\mathscr{CS}$ and canonical varieties follows the pattern of the structure of $Ψ$.
Ako citovať:
ISO 690:
Petrich, M. 2019. A conjecture for varieties of completely regular semigroups. In Mathematica Slovaca, vol. 69, no.3, pp. 541-556. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0246

APA:
Petrich, M. (2019). A conjecture for varieties of completely regular semigroups. Mathematica Slovaca, 69(3), 541-556. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0246
O vydaní:
Publikované: 21. 5. 2019