and ö. Hüseyin; Relative primeness of multidimensional polynomial matrices

A sufficient condition is given for the relative primeness (RP'ness) of two multidimensional polynomial matrices
A(s_1, \cdots ,s_p)
and
B(s_1,\cdots ,s_p)
of sizes
\sigma \times r
and
\kappa \times r
, such that (i)
\kappa + \sigma
is greater than
r
, (ii) there are
r
rows of
A(s_1, \cdots ,s_p)
and
B(s_1, \cdots ,s_p)
which form a nonsingular matrix. The sufficient condition is in the form of a rank test on a constant matrix having block Toeplitz structure and becomes both necessary and sufficient in the scalar case.