集合Λ上的简单半格Γ确定的二元关系半群P_Γ(Λ×Λ)的幂等元和极大子群  

Idempotents and maximal subgroups of semigroup P_Γ(Λ × Λ) of binary relations determined by the simple semilattice Γ on the set Λ

作　　者：林屏峰[1] LIN Ping-feng(School of Preparatory Courses, Southwest Minzu University, Chengdu 610041 ,P. R. C.)

机构地区：[1]西南民族大学预科教育学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2018年第3期326-330,共5页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：中央高校基本科研业务费专项项目(2015NZYQN38)

摘　　要：设Λ是任意的非空集合,Γ是集合Λ上的简单半格,P_Γ(Λ×Λ)是集合Λ上的简单半格Γ确定的二元关系半群,也是集合Λ上半格Γ确定的二元关系半群中的一类特殊的半群.首先通过简单半格的性质和利用集合Λ上半格Γ确定的二元关系半群的Green-关系已有的结论,刻画了半群P_Γ(Λ×Λ)的幂等元,从而得到半群P_Γ(Λ×Λ)的所有幂等元构成一个子半群.根据幂等元的结构,证明了半群P_Γ(Λ×Λ)的极大子群是由一个幂等元构成的单位元群.Let A be an arbitrary nonempty set, and F be a simple semilattice on the set A , PΓ（Λ×Λ） is a semigroup of binary relations determined by the simple semilattice Fon the set A , and also a kind of special semigroup in the binary relation semigroups determined by the semilattice on the set. In the semigroup PΓ（Λ×Λ）, by using the existing conclusions of the Green＇ s relations and properties of the simple semilattice, the idempotents are characterized, and the set of all idempotents forms a subsemigroup. According to the idempotent structure, it is proved that the maximal subgroup of the semigroup PΓ（Λ×Λ） is a unit group composed of an idempotent.

关 键 词：二元关系半群 集合上的简单半格 幂等元 链 极大子群 

分 类 号：O152.7[理学—数学]