TK-OPERATOR SEMIGROUPS FOR A CLASS OF E-UNITARY REGULAR SEMIGROUPS
Wang Li-min · Journal of South China Normal University · 2008
Four operators K,k,T and t are defined on the congruence lattice C(S) on a regular semigroup S as follows,for ρ∈S,ρK and ρk(ρT and ρt) are the greatest and the smallest congruences with the same kernel(trace) as ρ,respectively.The relations satisfied by operators K,k,T and t are determined as they act on congruence lattices of all E-unitary regular semigroups with that all their homomorphic images are E-unitary,and the quotient semigroup Γ+/Σ* is given.It is also determined that this TK-operator is a homomorphic image of Γ+/Σ*.