夹心半群S(X,Y,θ)上的α-同余

α-Congruences on the Sandwich Semigroups S(X, Y, θ )

本文讨论了夹心半群T(X,Y,θ)上的α-同余与集合Y上Tθ-等价关系之间的联系,证明了对于每个Tθ-等价关系E,夹心半群同余格C(T(X,Y,θ))的完全子格γ-1(E)中的最大元是一个α-同余,并判明Symons同余l,d都是α-同余.对于某些拓扑空间X,Y,确定了夹心半群S(X,Y,θ)上的最小(最大)真α-同余.

The relationship between the a-congruences on T(X, Y, θ) and the Tθ -equivalences on the set Y is investigated. It is proved that for each Tθ- equivalence E on Y, the greatest element in the complete sublattice γ-1(E) of C(T(X, Y, θ)) is an α-congruence. And it is verified that the Symons' congruences Z, d are two a-congruences for any sandwich semigroup. The smallest (greatest) α-congruences on S(X, Y, θ) are determined for some topological spaces X, Y.