Another Decomposition Theorem of Matrices over a Finite Distributive Lattice

In this paper, it is proved that a matrix over a finite distributive lattice can be decomposed into the sum of some matrices over finite chains whose number of elements are of the same. As a result, both the decomposition theorem of a matrix over a finite distributive lattice recently stated by Z.T. Fan and the decomposition theorem of a matrix over a finite chain in a paper of X.Z. Zhao, Y.B. Jun and F. Ren are generalized and extended. Further, by the decomposition theorem, the convergence index and period index of a matrix over a distributive lattice are studied and some new results are obtained.