On Factor Prime Factorizations for n-D Polynomial Matrices.

This paper investigates the problem of factor prime factorizations for n-D polynomial matrices and presents a criterion for the existence of factor prime factorizations for an important class of n-D polynomial matrices. As a by-product, we also obtain an algebraic algorithm to check n-D factor primeness in some important cases which partially solves the long-standing open problem of recognizing n-D factor prime matrices. Some problems related to the factorization methods are also studied. Several exam- pies are given to illustrate the results. The results presented in this paper are true over any coefficient field. [ABSTRACT FROM AUTHOR]