纯正半群上的强同余(I)

证明了纯正半群上的所有强同余构成该半群同余格的完备子格,刻画了与强同余对应的核-迹同余对-正规迹、正规子半群(称为强同余对)及其相互关系,由此给出纯正半群上任一强同余的结构,并证明强同余格和强同余对的集合之间一一对应.

Strong Congruence on an Orthodox Semigroup I

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.