SEMIGROUPS OF OPERATORS ASSOCIATED WITH THE KERNEL AND TRACE OF CONGRUENCES ON E-UNITARY COMPLETELY REGULAR SEMIGROUPS

Abstract

Let S be a regular semigroup and Con S the congruence lattice of S. For every ρ ε Con S there exist a greatest congruence ρ K [ρT] and a smallest congruence ρ k [ρt] on S with the same kernel [trace] as ρ. The subsemigroup Γ (S) of the transformation semigroup on Con S generated by the transformations ρ → ρK, ρ → ρk, ρ → ρT, and ρ → ρt, ρ ε Con S, is investigated for E-unitary completely regular semigroups. It is shown that in this case Γ(S′) contains 25 elements at most. A 25-element semigroup Γ(S′) is realized for some E-unitary regular orthogroup S′.