完全分配格和完备集环(英文)  

The Completely Distributive Lattices And The Complete Rings of Sets

作　　者：张玉琦[1] 

机构地区：[1]内蒙古师范大学离散数学研究所,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2003年第3期211-215,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

摘　　要：设L是完备格 ,S L称为L的基 ,若 x∈L ,Sx S使得 ∨Sx =x .称L是基拟原子的 ,若 x∈S且x≠ 1, y∈L ,使得x y因而x y .该文使用thewedgebelowrelation 证明 :完全分配格是完备集环当且仅当L有一个基S L使得L是基拟原子格 .又得到使用拓扑方法的如下刻划定理 :完全分配格是完备集环 L的区间拓扑θ(L) (Lawson拓扑λ(L)或双Scott拓扑σω(L) )Let L be a complete lattice.Then SL is called a basis of L iff x∈L,SxS satisfying ∨Sx=x,and L is called a basisquasiatomic lattice,if x∈S and x≠1,y∈L satisfying xy and so xy.This paper by using the wedge below relation  proves: A completely distributive lattice L is a complete ring of sets iff L has a basis SL so that L is a basisquasiatomic lattice.Again with the topological methods,we prove the topological characterization: A completely distributive lattice is a complete ring of sets iff the interval topology θ(L)(or the Lawson topology λ(L),or the double Scott topology σω(L)) of L is totally disconnected.

关 键 词：完全分配格 完备集环 基拟原子格 完备同余关系 完全并既约元 区间拓扑 

分 类 号：O153.1[理学—数学] O153.3[理学—基础数学]