摘要
主要讨论了格拟环的基本性质与凸子格拟环格 ,给出并证明了 :A)若L是一个格拟环 ,M是L的一个子拟环 ,则以下条件等价 :1)M是凸子格拟环 ;2 )M是凸的与定向的 ;3)M的右陪集R(M)是一个分配格 ,且 m1,m2 ∈L ,(M +m1) ∨ (M +m2 ) =M +m1∨m2 ,(M+m1) ∧(M+m2 ) =M+m1∧m2 .B)若L是一个格拟环 ,则C(L) ={M｜M是L的一个凸子格拟环 }是一个Brouwerian格 。
In this paper, the basic property and the lattice of all convex lattice ordered near ordered subnear rings of lattice ordered near rings are discussed, and the following theorems are given and proved:A) Let L be a lattice ordered near ring, the following are equivalent: 1) M is a convex lattice ordered subnear ring; 2) M is a convex and directive; 3) The right coset of M R(M) is a distributive lattice, moreover m 1,m 2∈L,(M+m 1)∨(M+m 2)=M+m 1∨m 2,(M+m 1)∧(M+m 2)=M+m 1∧m 2. B) Let L be a lattice ordered near ring, then C(L)=｛M｜M is a convex lattice ordered subnear ring｝ is a Brouwerian lattice, which is a sublattice of the lattice of all subnear rings of L.
出处
《湖南教育学院学报》
2000年第5期97-101,共5页
Journal of Hunan Educational Institute
关键词
子拟环
凸子格拟环格
格拟环
格群
有序拟环
lattice
near- ring
subnear ring
convex lattice-ordered subnear-ring
