Lattices of ∗-Congruences on a Quasi Regular ∗-Semigroup 1
Aixia Ding, Shiqun Li · 2009
In this paper, we define a relation θ by θ = {(ρ1 ,ρ 2) ∈ C ∗ (S) × C ∗ (S) : Ptrρ1 = Ptrρ2} on the complete lattice C ∗ (S )o f∗-congruences under set inclusion relation on a quasi regular ∗-semigroup S. We prove that θ is a congruence on C ∗ (S) and each θ-class is a complete sublattice of C ∗ (S). The largest ∗-congruence of each θ-class and the largest projection separating ∗-congruence on S are characterized. We also consider the projection kernel normal systems of the meet and union of the regular ∗-congruences ρ and σ on S, where (ρ, σ) ∈ θ.