Petrychkovych Vasyl' Mykhajlovych
Scientific degree: Doctor of sciences in physics and mathematics (01.01.06 – algebra and number theory, 2006)
Scientific title: Professor
Position: Head of Department of algebra
In Institute: from 1971
Research
interests:
-
Theory of
ring, matrix rings;
-
Linear algebra, matrix polynomial,
matrix equations and its applications
Major publications:
Monograph:
Generalized equivalence of matrices and its
collections and factorization of matrices over
rings. - L'viv: Pidstryhach Institute
for Applied Problems
of Mechanics and Mathematics of the NAS
of Ukraine, 2015. – 312 p. pdf
Research
Articles:
1. The structure of solutions of the matrix linear unilateral polynomial equation with two variables (with Dzhaliuk N.S.). Carpathian Math. Publ. – 2017. – 9, No. 1. – 10 p.
2.
Equivalence
of pairs of matrices with relatively prime determinants over quadratic rings of
principal ideals (with Ladzoryshyn N.B.). Bulet. Acad. de Stinte Republ.
3.
Absolute factorization of
matrices in the rings of
block-triangular matrices (with
4. The matrix linear unilateral and bilateral equations with two variables over commutative rings. (with Dzhaliuk N.S) // ISRN Algebra, Volume 2012, Article ID 205478, 14 pages, doi: 10.5402/2012/205478.
5. Seniscalar equivalence of polynomial matrices and tne solutions of the Sylvester matrix polynomial equations. (with Dzhaliuk N.S). Mathematical bulletin of the Shevchenko scientific society. 9, 81–88, (2012).
6. Solutions of matrix polynomial diophantine equation (with Dzhaliuk N.S). Applied problems of mechanics and mathematics. 10, 55 – 61, (2012).
7. The matrix diophantine equations AX+ BY= C (with Dzhaliuk N.S). Carpathian Mathematical Publications 3 (2), 49–56, (2011).
8. Parallel factorizations of matrices over rings and their connections (with Dzhaliuk N.S). Applied problems of mechanics and mathematics. 8, 7 – 17, (2010).
9. On the stable range of matrix rings (with Zabavsky B.V.). Ukrainian Mathematical Journal 61 (11), 1853–1857, (2009).
10. On solvents of matrix polynomial equations and their number. Applied problems of mechanics and mathematics. 7, 52 – 56, (2009).
11. Factorization of block diagonal and block triangular matrices over principal ideal rings (with Dzhaliuk N.S). Mathematical bulletin of the Shevchenko scientific society. 4, 79–89, (2007).
12. On equivalence of matrices over quadratic Euclidean rings (with Zelisko V.R., Ladzoryshyn N.B.). Applied problems of mechanics and mathematics. 4, 16 – 21, (2006).
13. Multiplicities of characteristic roots, degrees of elementary divisors and factorization of polynomial matrices. Mat. Metody Fiz.-Mekh. Polya 48, (2), 7–17, (2005).
14. On solutions of matrix polynomial equations and the similarity of matrices. Mat. Metodi Fiz.-Mekh. Polya. 48, ( 4), 14–19, (2005).
15. On solution of matrix polynomial equations and on similarity of matrices (with Dzhaliuk N.S). Mat. Metody Fiz.-Mekh. Polya. 48, ( 4), 14 – 19, (2005).
16. Generalized equivalence of collections of matrices and common divisors of matrices. Algebra and Discrete Mathematics. 2, 84 – 91, (2004).
17. On common divisors of polynomial matrices (with Zelisko V.R.) . Applied problems of mechanics and mathematics. 2, 56 – 60, (2004).
18. On divisibility and factorization of matrices. Mat. Stud. 22, ( 2), 115-120 (2004).
19. Standard form of pairs of matrices with respect to generalized equivalence. Visnyk Lviv. Univ., Ser. Mech-Math. 61, 148 – 155, (2003).
20. Structure-theoretical properties of matrices finitely generated principal ideal rings (with Komarnytsky N.Ya.). Mat. Metody Fiz.-Mekh. Polya. 46, (2), 7 – 21, (2003).
21.
On common monic
divisors of polynomial matrices with given canonical
diagonal form, (with Dzhaliuk N.S). Mat.
Metody Fiz.-Mekh. Polya . 45, ( 3), 7 – 13, (2002).
22.
Generalized equivalence of pairs of matrices. Linear and Multilinear Algebra. 48, (2), 179 – 188, (2000).
23.
Reducibility of pairs
of matrices by generalized equivalent transformations to triangular and
diagonal forms and their applications. Mat. Metody Fiz.-Mekh.
Polya. 43, ( 2),
15 – 22, (2000).
24.
A criterion of diagonalizability
of a pair of matrices over the ring of principal ideals by common row and separate
column transformations.Ukr. Math. J. 49, (6), 963–965, (1997).
25.
Generalized equivalence of pairs of matrices. . Mat. Stud. 8, (2),
147 – 152, (1997).
26.
On the parallel
factorization of matrices over principal ideal rings Journal of Mathematical Sciences,
27.
Parallel
factorizations of polynomial matrices. Ukrainian Mathematical Journal 44
(9), 1123–1127, (1992).
28.
Semiscalar equivalence and the
factorization of polynomial matrices Ukrainian Mathematical Journal. 42, (5),
570–574, (1990).
29. Decomposition of polynomial matrices into factors with prescribed canonical diagonal forms Journal of Soviet Mathematics. 64 (5), 1129–1131, (1993).
30. Semiscalar equivalence and the Smith normal form of polynomial matrices Journal of Soviet Mathematics. 66, No.1, 2030–2033, (1993).
31.
Factorization of
polynomial matrices over arbitrary fields. (with Prokip V.M.) Ukrainian Mathematical
Journal. 38, (4), 409–412, (1986).
32.
Cell-triangular
and cell-diagonal factorizations of cell-triangular and cell-diagonal
polynomial matrices. Mathematical Notes. 37, 431–435, (1985).
33.
Linear divisors and
reducibility of polynomial matrices. Ukrainian Mathematical
Journal. 36,
(2) 176–181,
(1984).
34.
Problems of the factorization of matrix polynomials.
Mat. Metody Fiz.-Mekh. Polya 14, 19–26, (1981).
35.
On the number of solutions of a matrix equation. Mat. Metody Fiz.-Mekh. Polya 12, 56–58, (1980).
36.
Absolute expansibility of matrix polynomials Mat. Metody
Fiz.-Mekh. Polya 9, 37–41, (1979).
37. Decomposability of polynomial matrices into a product of linear factors (with Kazimirs' kii PS). Mat. Met. Fiz.-Mekh. Polya. 8, 3 – 9, (1978).
1. On the equivalence of polynomial matrices (with Kazimirs' kii PS). Theoretical and Applied Problems of Algebra and Differential Equations. 61 – 66, (1977).
E-mail: vpetrych@iapmm.lviv.ua