Monic divisors of polynomial matrices over infinite field
Algebra and discrete mathematics, Tome 12 (2011) no. 2, pp. 94-101.

Voir la notice de l'article provenant de la source Math-Net.Ru

The necessary and sufficient conditions of existence of monic divisors of a nonsingular polynomial matrix over an infinite field are established.
Keywords: monic divisors of polynomial matrices
Mots-clés : canonical diagonal form of polynomial matrices.
@article{ADM_2011_12_2_a8,
     author = {Andriy Romaniv},
     title = {Monic divisors of polynomial matrices over infinite field},
     journal = {Algebra and discrete mathematics},
     pages = {94--101},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a8/}
}
TY  - JOUR
AU  - Andriy Romaniv
TI  - Monic divisors of polynomial matrices over infinite field
JO  - Algebra and discrete mathematics
PY  - 2011
SP  - 94
EP  - 101
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a8/
LA  - en
ID  - ADM_2011_12_2_a8
ER  - 
%0 Journal Article
%A Andriy Romaniv
%T Monic divisors of polynomial matrices over infinite field
%J Algebra and discrete mathematics
%D 2011
%P 94-101
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a8/
%G en
%F ADM_2011_12_2_a8
Andriy Romaniv. Monic divisors of polynomial matrices over infinite field. Algebra and discrete mathematics, Tome 12 (2011) no. 2, pp. 94-101. http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a8/

[1] Gochberg I., Lancaster P., Rodman L., Matrix Polynomials, Academic Press, New York, 1982, 409 pp. | MR

[2] A.N. Malyshev, “Factorization of matrix polynomials”, Sib. Math. J., 23:3 (1982), 136–146 | MR | Zbl

[3] P.S. Kazimirskij, “A Solution to the problem of separating a regular factor from a matrix polynomial”, Ukr. Math. Zh., 32:4 (1980), 483–498 | MR

[4] P.S. Kazimirskij P.S., V.M. Petrychkovych, “About equivalence of polynomial matrices”, Theoretical. and prikl. questions of algebra and differential equations, Science. Opinion, Kyiv, 1977, 61–66

[5] V.R. Zelisko, “On the structure of some class of invertible matrices”, Mat. Met. and Fiz.-Mekh. Fields, 1980, no. 12, 14–21 | MR | Zbl

[6] M. Slusky, Zeros of $2\times2$ Matrix Polynomials, 5 Dec., 2009, arXiv: 0912.1030v1[math.RA] | MR | Zbl

[7] J. Maroulas, P. Psarrakos, “On factorization of matrix polynomials”, Linear Algebra and its Applications, 2000, no. 304, 131–139 | DOI | MR | Zbl

[8] N.S. Dzhaluk, V.M. Petrychkovych, “On common monic divisors of polynomial matrices with given canonical diagonal form”, Mat. Met. and Fiz.-Mekh. Fields, 45:3 (2002), 7–13 | MR

[9] A.M. Romaniv, “Unital divisors with one invariant factor of polynomial matrices”, Mat. Met. and Fiz.-Mekh. Fields, 53:4 (2010), 35–43 | MR | Zbl

[10] Newman M., Integral Matrices, Academic Press, New York, 1972, 224 pp. | MR | Zbl

[11] V.P. Shchedryk, “Factorization of matrices over elementary divisor rings”, Journal Algebra and Discrete Mathematics, 2009, no. 2, 79–98 | MR | Zbl

[12] V.P. Shchedryk, “On one class of matrix divisors”, Mat. Met. and Fiz.-Mekh. Fields, 40:3 (1997), 13–19

[13] V.P. Shchedryk, “A class of divisors of matrices over a commutative elementary divisor domain”, Matematychni Studii, 17:1 (2002), 23–28 | MR | Zbl

[14] V.M. Petrychkovych, “On decomposition matrix polynomials in the product of monic factors”, Algebra and topology, Thematic coll. sat. science. papers, Lviv State University, Lviv, 1996, 112–124