Publication details

On singleton kernel classes in the lattice of varieties of completely regular semigroups

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Authors

KAĎOUREK Jiří

Year of publication 2019
Type Article in Periodical
Magazine / Source International Journal of Algebra and Computation
MU Faculty or unit

Faculty of Science

Citation
web https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541
Doi http://dx.doi.org/10.1142/S0218196719500541
Keywords Completely regular semigroups; varieties of completely regular semigroups; kernel and trace classes in the lattice of varieties of completely regular semigroups; relatively free completely regular semigroups.
Description In this paper, it is shown that, for every non-trivial variety U of groups, the variety HU of all completely regular semigroups all of whose subgroups belong to U is minimal in its kernel class in the lattice L(CR) of all varieties of completely regular semigroups, and hence it constitutes, in fact, a singleton kernel class in the lattice L(CR). Even more generally, it is shown that, for every variety V of completely simple semigroups which does not consist entirely of rectangular groups, the variety DV of all completely regular semigroups all of whose completely simple subsemigroups belong to V is minimal in its kernel class in the lattice L(CR), and hence it likewise constitutes a singleton kernel class in the mentioned lattice L(CR).
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