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@article{1634742,
author = {Kaďourek, Jiří},
article_location = {Singapore},
article_number = {8},
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.},
language = {eng},
issn = {0218-1967},
journal = {International Journal of Algebra and Computation},
title = {On singleton kernel classes in the lattice of varieties of completely regular semigroups},
url = {https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541},
volume = {29},
year = {2019}
}
TY - JOUR
ID - 1634742
AU - Kaďourek, Jiří
PY - 2019
TI - On singleton kernel classes in the lattice of varieties of completely regular semigroups
JF - International Journal of Algebra and Computation
VL - 29
IS - 8
SP - 1383-1407
EP - 1383-1407
PB - World Scientific
SN - 02181967
KW - Completely regular semigroups
KW - varieties of completely regular semigroups
KW - kernel and trace classes in the lattice of varieties of completely regular semigroups
KW - relatively free completely regular semigroups.
UR - https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541
L2 - https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541
N2 - 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).
ER -
KAĎOUREK, Jiří. On singleton kernel classes in the lattice of varieties of completely regular semigroups. \textit{International Journal of Algebra and Computation}. Singapore: World Scientific, 2019, vol.~29, No~8, p.~1383-1407. ISSN~0218-1967. Available from: https://dx.doi.org/10.1142/S0218196719500541.
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