Separating a unital divisor from a rectangular polynomial matrix

It is required to separate a unital divisor with a preassigned characteristic polynomial from a rectangular polynomial matrix over a field. Necessary and sufficient conditions of existence, under certain restrictions, are obtained for such a divisor, as well as a method for constructing it. By the approach used in this paper it is possible to completely solve this problem for rectangular polynomial matrices, all of whose elementary divisiors are pair-wise relatively prime. The results obtained are illustrated by solving matrix equations.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1089–1094, August, 1990.