Abstract
On the congruence lattice (2(5) of a completely regular semigroup S the following mappings are considered χp: ρ → ρ ∩P and χp: ρ VP, whereP is any of the Green relationsH, L, R orD. The equivalence relationsP Λ 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 Λ,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 Λ 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.
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References
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Petrich, M. The Green relations approach to congruences on completely regular semigroups. Annali di Matematica pura ed applicata 167, 117–146 (1994). https://doi.org/10.1007/BF01760331
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DOI: https://doi.org/10.1007/BF01760331