集合Λ上的半格Γ确定的二元关系半群P_Γ(Λ×Λ)的不可分解元

Non-solvabla elements of semigroup P_Γ(Λ × Λ) of binary relations determined by the semilattice Γ on the set Λ

设Λ是任意的非空集合,Γ是集合Λ上的半格,PΓ(Λ×Λ)是集合Λ上的半格Γ确定的二元关系半群。得到了半群PΓ(Λ×Λ)的不可分解元的一个充分必要条件,并且在一定条件下找到了一类不可分解元。

Let Λ be an arbitrary nonempty set,and Γ be a semilattice on the set Λ. Let PΓ（ Λ × Λ） is a semigroup of binary relations determined by the semilattice Γ on the set Λ. In the semigroup PΓ（ Λ × Λ）,a necessary and sufficient condition of non-solvable elements is obtained,and a class of non-solvable elements is found under certain conditions.