夹心半群T_E(X,Y,θ)上的一个同余

A Congruence on the Sandwich Semigroups T_E(X,Y,θ)

摘要: 对于Y上的任意非平凡等价关系E,讨论了由E确定的夹心半群TE(X,Y,θ)的同余格C(TE(X,Y,θ)),证明了当θ是单射时,C(TE(X,Y,θ))可分解为3个不相交的完全子格C(δ),Cα(δ),C(E),Cα(E)和C(ω),Cα(ω).在此基础上考察了TE(X,Y,θ)上的一个同余τ,并证明了当E为单等价关系时,τ是C(E),Cα(E)中的唯一原子.

Abstract: The congruence lattice C(TE(X,Y,θ)) on sandwich semigroups TE(X,Y,θ) determined by any nontrivial equivalence E on Y is discussed.It is proved that C(TE(X,Y,θ)) can be decomposed into three disjoint complete sublattices C(δ),Cα(δ),C(E),Cα(E) and C(ω),Cα(ω) when θ is injection.Based on above,a congruence τ on TE(X,Y,θ) is searched,and it is proved that τ is a unique atom in C(E),Cα(E) when E is simple equivalence.