Publication details
On singleton kernel classes in the lattice of varieties of completely regular semigroups
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Algebra and Computation |
| MU Faculty or unit | |
| 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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