The Greatest Idempotent-separating Congruence and Group Congruences on a Weakly Inverse Semigroup
Bing Yu · Journal of Sichuan Normal University · 2001
In this paper, the greatest idempotent separating congruence and the minimum group congruence on a weakly inverse semigroup S are characterized. It is proved therefore that the lattice of group congruences on S is complete lattice isomorphic to the lattice of group congruences on I(S) , the inverse subsemigroup of principal elements of S . Moreover, the lattice of group congruences of S is also a lattice homomorphic image of the lattice of all congruences of S .