Strong Congruence on an Orthodox Semigroup I
Zhu Jin-hua · Journal of Sichuan Normal University · 2005
The aim of this paper is to study inverse semigroup congruence on an orthodox semigroup S(which we called it strong). It is proved that the set C()P()(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., normal traces, normal subsemigroups as well as the relationship between them (called strong congrunce pairs) are characterized. By using these, a structure theorem for an arbitrary strong congruence on S is given. It is also proved that there exists a bijection between the lattice C()P()(S) and the set of all strong congrunce pairs of the orthodox semigroiup S.