Another lattice of varieties of completely regular semigroups
Mario Petrich ยท Communications in Algebra ยท 2016
Completely regular semigroups S are taken here with the unary operation of inversion within the maximal subgroups of S. As such they form a variety ๐โ whose lattice of subvarieties is denoted by โ(๐โ). The relation on โ(๐โ) which identifies two varieties if they contain the same bands is denoted by Bโง. The upper ends of Bโง-classes which are neither equal to ๐โ nor contained in the variety ๐๐ฎ of completely simple semigroups are generated by two countably infinite ascending chains called canonical varieties. In a previous publication, we constructed the sublattice ฮฃ of โ(๐โ) generated by ๐๐ฎ and the first four canonical varieties. Here we extend ฮฃ to the sublattice ฮจ of โ(๐โ) generated by ๐๐ฎ and the first six canonical varieties. For each of the varieties in ฮจโฮฃ, we construct the ladder and a basis of its identities.