Informace o publikaci
On singleton kernel classes in the lattice of varieties of completely regular semigroups
| Autoři | |
|---|---|
| Rok publikování | 2019 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | International Journal of Algebra and Computation |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541 |
| Doi | http://dx.doi.org/10.1142/S0218196719500541 |
| Klíčová slova | 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. |
| Popis | 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). |
| Související projekty: |