Mathematica Bohemica

Mathematica Bohemica, Vol. 145, No. 1, pp. 1-14, 2020

A semilattice of varieties of completely regular semigroups

Mario Petrich

Received October 6, 2017. Published online November 15, 2018.

Abstract: Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by $\mathcal L(\mathcal C\mathcal R)$. We construct a 60-element $\cap$-subsemilattice and a 38-element sublattice of $\mathcal L(\mathcal C\mathcal R)$. The bulk of the paper consists in establishing the necessary joins for which it uses Polák's theorem.

Keywords: completely regular semigroup; lattice; variety; $\cap$-subsemilattice

Classification MSC: 20M07

DOI: 10.21136/MB.2018.0112-17

PDF available at: Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Mario Petrich, 21420 Bol, Brač, Croatia

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