A generalized Serre problem (Q1882990)

\textit{Z. Lin} and \textit{N. K. Bose} [Linear Algebra Appl. 338, No. 1--3, 125--138 (2001; Zbl 1017.13006)] established the equivalence of several generalizations of the well-known Serre conjecture. The article under review proposes a proof for the first of these generalizations (in matrix form) based on the Serre conjecture itself (proved in 1976). In so doing, the Grassmannian scheme and Plücker embedding are used. Other recent papers related to this topic: \textit{J. F. Pommaret}, ``Solving Bose conjecture on linear multidimensional systems'', in: Proc. European Control Conf. 2001 (CD-ROM) and \textit{H. A. Park}, ``Prime factorization of \(N\)-\(D\) polynomial matrices'', in: Proc. IEEE Int. Conf. Circuits and Systems, Vol. 3, 666--669 (2003).