The Rows And Columns Space Lattice Of Two Products Of Boolean Matrices

In this paper,first,we consider the Boolean matrix on the binary Boolean algebra,and give a representation of finite lattice by the rows and columns space of the Boolean matrix,the rows and columns space lattice,and discuss its factor structure by means of congruence matrices and describe the interrelations between factor lattices,congruences and such matrices.Then we prove that the rows and columns space lattice of the Kronecker product of Boolean matrices is isomorphic to the tensor product of rows and columns space lattices of Boolean matrices.This fact is used to prove some properties of tensor products of finite lattices.Then we show that in which case a pair of sublattices（L₁,L₂）of a finite lattice L is a subtensor product decomposition of L.Next,we defined the substitution sum of Boolean matrices,according to the substitution sum of Boolean matrices,the substitution product of finite lattice is defined.It is proved that the rows and columns space lattice of the substitution sum of Boolean matrices is isomorphic to the substitution product of their rows and columns space lattice,and a decomposition theorem of such product is given.