Strong Congruences on Regular Semigroups
Bingjun Yu · Journal of Sichuan Normal University · 2007
The aim of this paper is to study inverse semigroup congruences on an arbitrary regular semigroup S called strong congruence.It is proved that the set SC(S) of all strong congrunces on S forms a complete sublattice of the congruence lattice C(S) of S.Furthermore,the kernel-trace congrunce pairs corresponding to the strong congruences,i.e.,strong congrunce pairs as well as the relationship between them are characterized.By using these,a structure theorem for strong congruences on S is given.It is also proved that there exists a bijection between the lattice SC(S) and the set of all strong congrunce pairs of the regular semigroup S.