| 布尔格的主同余 |
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| 引用本文： | 曹发生.布尔格的主同余[J].四川师范大学学报(自然科学版),2012(2):236-239. |
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| 作者姓名： | 曹发生 |
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| 作者单位： | 毕节学院数学系;中山大学逻辑与认知研究所 |
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| 基金项目： | 贵州省教育厅自然科学基金(黔教科20090068)资助项目 |
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| 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.
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| 关 键 词： | 主同余 布尔格 基数 |
Principal Congruence on Boolean Lattices |
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| CAO Fa-sheng.Principal Congruence on Boolean Lattices[J].Journal of Sichuan Normal University(Natural Science),2012(2):236-239. |
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| Authors: | CAO Fa-sheng |
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| Institution: | CAO Fa-sheng1,2(1.Department of Mathematics,Bijie College,Bijie 551700,Guizhou; 2.Institute of Logic and Cognition,Sun Yat-sen University,Guangzhou 510275,Guangdong) |
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| Abstract: | 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. |
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| Keywords: | principal congruence boolean lattice cardinal number |
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