布尔格的主同余  

Principal Congruence on Boolean Lattices

作　　者：曹发生[1,2] 

机构地区：[1]毕节学院数学系,贵州毕节551700 [2]中山大学逻辑与认知研究所,广东广州510275

出　　处：《四川师范大学学报（自然科学版）》2012年第2期236-239,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：贵州省教育厅自然科学基金(黔教科20090068)资助项目

摘　　要：基于布尔格的次直积同构表示,引入布尔格的元的不可辨下标集的定义,给出布尔格的元的不可辨下标集的简单性质.应用布尔格的元的不可辨下标集给出布尔格的主同余的刻画,并给出有穷布尔格的主同余的基数与布尔格的元的不可辨下标集的基数的联系,从而得到布尔格的主同余的构造方法.Congruences,which are closely related to quotient algebras,play an important role in algebra theory.The researchers study the lattices which are the sets of all congruences with subsumption relation.Principal congruences as special congruences are concerned.The indiscernible index set for elements of Boolean lattices is defined based on isomorphism representation of subdirect product on Boolean lattices,and the simple properties of them are discussed.Then equivalent characterization for principal congruence on Boolean lattices is obtained by the indiscernible index set for elements of Boolean lattices.Finally,the relationship of cardinal number of the indiscernible index set and principal congruence on finite Boolean lattices is studied.The construction methods for principal congruences on Boolean lattices are obtained.

关 键 词：主同余 布尔格 基数 

分 类 号：O153.5[理学—数学]