To solving multiparameter problems of algebra. 7. The PG-q factorization method and its applications

The paper continues the development of rank-factorization methods for solving certain algebraic problems for multi-parameter polynomial matrices and introduces a new rank factorization of a q-parameter polynomial m × n matrix F of full row rank (called the PG-q factorization) of the form F = PG, where is the greatest left divisor of F; Δ _i ^(k) i is a regular (q-k)-parameter polynomial matrix the characteristic polynomial of which is a primitive polynomial over the ring of polynomials in q-k-1 variables, and G is a q-parameter polynomial matrix of rank m. The PG-q algorithm is suggested, and its applications to solving some problems of algebra are presented. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 150–163.