弱逆半群上最大幂等元分离同余和群同余

The Greatest Idempotent-separating Congruence and Group Congruences on a Weakly Inverse Semigroup

刻画了弱逆半群S上的最大幂等元分离同余和最小群同余 .在此基础上 ,证明了S的群同余格与S的由主元所组成的逆半群I(S)的群同余格完备格同构 ;进而 ,证明了I(S)的群同余格是S的同余格的格同态像 .

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 .