Matrix Representation of Finite Distributive Lattices
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.
Boolean matrixPartial order relation matrixRow and column space latticeCongruence matrixCongruence relation
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