Geodesic
To solving multiparameter problems of algebra. 7. The $PG$-$q$ factorization method and its applications
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 150-163 
V. N. Kublanovskaya. To solving multiparameter problems of algebra. 7. The $PG$-$q$ factorization method and its applications. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 150-163. http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a10/
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     author = {V. N. Kublanovskaya},
     title = {To solving multiparameter problems of algebra.~7. {The} $PG$-$q$ factorization method and its applications},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a10/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper continues the development of rank-factorization methods for solving certain algebraic problems for multiparameter polynomial matrices and introduces a new rank factorization of a $q$-parameter polynomial $m\times n$ matrix $F$ of full row rank (called the $PG$-$q$ factorization) of the form $F=PG$, where $P=\prod\limits^{q-1}_{k=1}\prod\limits^{n_k}_{i=1}\nabla^{(k)}_i$ is the greatest left divisor of $F$; $\nabla^{(k)}_i$ 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.

[1] V. N. Kublanovskaya, “To solving multiparameter problems of algebra, 5”, Zap. Nauchn. Semin. POMI, 309, 2004, 144–153 | MR | Zbl

[2] V. N. Kublanovskaya, “To solving multiparameter problems of algebra, 2”, Zap. Nauchn. Semin. POMI, 296, 2003, 89–107 | MR | Zbl

[3] V. N. Kublanovskaya, V. B. Khazanov, “Relative factorization of polynomials in several variables”, Zh. Vychisl. Matem. Mate. Fiz., 36:8 (1996), 6–11 | MR | Zbl

[4] V. B. Khazanov, “On spectral properties of multiparameter polynomial matrices”, Zap. Nauchn. Semin. POMI, 229, 1995, 284–321 | MR | Zbl

[5] V. N. Kublanovskaya, “An approach to solving multiparameter problems”, Zap. Nauchn. Semin. POMI, 229, 1995, 191–246 | MR

[6] V. N. Kublanovskaya, “To solving multiparameter problems of algebra, 6”, Zap. Nauchn. Semin. POMI, 323, 2005, 132–149 | MR | Zbl