The Green relations approach to congruences on completely regular semigroups

On the congruence lattice (2(5) of a completely regular semigroup S the following mappings are considered _p: P and _p: VP, whereP is any of the Green relationsH, L, R orD. The equivalence relationsP andP ^V induced by these maps represent the main object of study in the paper. The former is a complete -congruence whereas the latter is a complete congruence onC(S). In particularH ,H ^V,L ^V,R ^V coincide with the kernel, trace, left trace and right trace relations onC(S), respectively. All essential properties known for the latter relations carry over to the new relationsP andP ^V. In addition, some interesting interplays of these provide for more richness in the theory of congruences on completely regular than is the case for the kernel-trace approach to congruences on regular semigroups.