A Note on Strong P-Congruence Lattices of P-Regular Semigroups
Zenghui Gao · Journal of Sichuan Normal University · 2004
Let S(P) be a PBX-regular semigroup. In this paper, it is proved that the strong P-congruence lattice and strong P-congruence-pair lattice of S(P) are isomorphic. Moreover the θ-relation is defined by so-called c-trace on the strong P-congruence lattice Λ_P(S). Further, a characterization of strong P-kernel normal systems is given for the join and meet of two strong P-congruences which are in the same θ-class. Finally, it is also proved that the strong P-congruence lattice and the lattice of strong P-kernel normal systems on S(P) are isomorphic. The results obtained here deepened some relative results in recent literature.