有限分配格的矩阵表示  

Matrix Representation of Finite Distributive Lattices

作　　者：罗从文[1] 梅华鑫 LUO Cong-wen;MEI Hua-xin(College of Science,China Three Gorges University,Yichang,Hubei,443002,China)

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《模糊系统与数学》2024年第2期55-61,共7页Fuzzy Systems and Mathematics

基　　金：湖北省教育厅科技研究资助项目(B2016016)。

摘　　要：在本文中,我们考虑二元布尔代数上的布尔矩阵,提出了n阶布尔矩阵的保关联关系映射和降集的定义,证明了n阶偏序关系矩阵的列空间格和其降集格同构,得到了有限分配格的矩阵表示定理,通过同余矩阵刻划了有限分配格的同余关系.In this paper,we consider the Boolean matrix on a binary Boolean algebra,and propose the definitions of preserving incidence relation mappings and down sets of n-th order Boolean matrix,we prove the column space lattice is isomorphism to the lattice of down sets of some n-th order partial order relation matrix,obtain the matrix representation theorem of a finite distributive lattice,we characterize the congruences of a finite distributive lattice by congruence matrices.

关 键 词：布尔矩阵 偏序关系矩阵 行列空间格 同余矩阵 同余关系 

分 类 号：O159[理学—数学]