Factorizations of matrices over semirings

In this paper, as a generalization of prime Boolean matrices and prime fuzzy matrices, we study semiprime matrices over chain semirings using the relationship between semiprime matrices and their row spaces. We show that a nonmonomial matrix with full semiring rank can be expressed as a product of elementary matrices and semiprime matrices. Furthermore, we show that a nonmonomial, regular matrix with full semiring rank can be expressed as a product of elementary matrices.