The lattice of completely regular semigroup varieties
Francis J. Pastijn · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1990
Abstract A completely regular semigroup is a semigroup which is a union of groups. The class CR of completely regular semigroups forms a variety. On the latticeL(CR) of completely regular semigroup varieties we define two closure operations which induce complete congruences. The consideration of a third complete congruence onL(CR) yields a subdirect decomposition ofL(CR). Using these results we show thatL(CR) is arguesian. This confirms the (tacit) conjecture thatL(CR) is modular.