二元关系半群P_Γ(Λ×Λ)的一类左单位的构造

Construction of a class of left unit of semigroup P_Γ( Λ × Λ)

设Λ是任意的非空集合,Γ是集合Λ上的半格,f:Λ→Γ是任意集值变换.通过Λ上的极值变换f定义集合Λ上由半格Γ确定的二元关系,而P_Γ(Λ×Λ)是集合Λ上由半格Γ确定的所有二元关系构成的集合,并且P_Γ(Λ×Λ)在二元关系的乘积运算构成半群.利用半群P_Γ(Λ×Λ)左单位已有的结论,以及二元关系之间的包含关系,可以获得P_Γ(Λ×Λ)的一类左单位的重要特征,从而可以构造出半群P_Γ(Λ×Λ)的一类左单位.

Let A be an arbitrary nonempty set, and F be a semilattice on the set A. Let f be an arbitrary transformation of the set A into the set Г. On the set A , by transformation f, a binary relation determined by the semilattice F is defined, and all of these binary relations constitute the set PГ（∧×∧）. In the multiplication of binary relations, PГ（∧×∧） is a semigroup. In the semigreup PГ（∧×∧） , by using the existing conclusions of left units, and the inclusion relations between the binary relation, the important properties of left units are obtained. As a result, a class of left units is constructed.