Factorizability conditions for multidimensional polynomials

In this paper, new results concerning the factorizability of multidimensional polynomials are presented. Necessary and sufficient conditions for the factorizability or separation of a given
m
-D (
m
- dimensional) polynomial into: 1)
m
1-D polynomials, and 2) a number of multidimensional polynomials of appropriate dimensions are explicitly formulated.