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

Abstract

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 $P = \prod\limits_{k = 1}^{q - 1} {\prod\limits_{i = 1}^{n_k } {\nabla _i^{(k)} } }$ is the greatest left divisor of F; Δ ^(k)_i 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.