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 represen-tation theorem of a finite distributive lattice,we characterize the congruences of a finite distributive lattice by congru-ence 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
Key words
Boolean matrix/Partial order relation matrix/Row and column space lattice/Congruence matrix/Congruence relation
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