The class CR of completely regular semigroups equipped with the unary operation of inversion forms a variety whose lattice of subvarieties is denoted by L(CR). The variety B of all bands induces two relations B∧ and B∨ by meet and join with B. Their classes are intervals with lower ends VB∧ and VB∨ , and upper ends VB∧ and VB∨ . These objects induce four operators on L(CR).The cluster at a variety V is the set of all varieties obtained from V by repeated application of these four operators. We identify the cluster at any variety in L(CR).

EB00000003198K

Available