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.
Equivalence of matrices in the ring M(n,R) and its subrings. (with Dzhaliuk N.S.) Ukrainian Mathematical Journal. 73, No.12, 1865– 1872, (2022). https://doi.org/10.1007/s11253-022-02034-0.
2.
The number of standard forms of matrices over imaginary Euclidean
quadratic rings with respect to the (z,k)-equivalence.
(with Ladzoryshyn N.B.) Mat. Stud. 57, No. 2, 115–121, (2022).
3.
On standard forms of pairs of matrices over the
ring of gaussian integers with respect to (z,k)-equivalence. (with Ladzoryshyn N.B.) Mat. Metody Fiz.-Mekh. Polya 64,
(4), 18–24, (2021) (in Ukrainian).
4.
Equivalence of matrices in the ring M(n,R) and in its subrings. (with
5.
Standard form of matrices over quadratic
rings with respect to the (z,k)-equivalence and the structure of solutions of bilateral
matrix linear equations. (with Ladzoryshyn N.B.) Journal of Mathematical Sciences, Vol. 253, No. 1, February, 54–62 (2021). DOI 10.1007/s10958-021-05212-w
6.
Matrix Diophantine equations over quadratic
rings and their solutions. (with Ladzoryshyn N.B. and Zelisko H. V.) Carpathian Math. Publ. 12, (2), 340–347. (2020).
7.
The standard form of
matrices over the ring of
gaussian integers with respect to
(z, k)-equivalence. (with
Zelisko H.V. and Ladzoryshyn
N.B.) Applied problems of
mechanics and mathematics. 18, 5–10, (2020). –
https://doi.org/10.15407/apmm2020.18.5-10. (in Ukrainian)
8.
Standard forms of matrices
over rings with respect to different types of equivalences
and their applications in theory of the matrix
factorization and matrix equations. Mat. Metody Fiz.-Mekh. Polya 62,
(4), 7–27, (2019).
9.
Solutions of the matrix linear bilateral
polynomial equation and their
structure. (with Dzhaliuk N.S.) Algebra and Discrete
Mathematics. 27, (2), 243–251, (2019).
10.
The standard form of matrices over
quadratic rings with respect to (z,k)-equivalence and structure of solutions
of matrix bilateral linear equations. (with Ladzoryshyn N.B.). Mat. Metody Fiz.-Mekh. Polya. 61, (2), 49–56, (2018).
11.
Matrix linear unilateral and bilateral equations
over quadratic rings. (with Ladzoryshyn N.B.). Visnyk of the Lviv
Univ. Series Mech. Math. 85, 32–40, (2018).
12.
Factorizations in the rings of
the block matrices. (with Dzhaliuk N.S.). Bul. Acad. Stiinte Repub. Mold. Mat. 85 (3), 23–33, (2017).
13.
Factorizations in the matrix ring
and its subrings
of the block
matrices (with Dzhaliuk N.). Proceedings the Fourth Conference of Mathematical Society of the
Republic of Moldova: dedicated to the centenary
of Vladimir Andrunachievici (1917–1997). Chisinau, 143–146, (2017).
14. The structure of
solutions of the matrix linear unilateral polynomial equation with two
variables. (with Dzhaliuk N.S.). Carpathian Math.
Publ. 9, (1), 48–56, (2017).
15. Equivalence of pairs
of matrices with relatively prime determinants over quadratic rings of
principal ideals. (with Ladzoryshyn N.B.). Bulet. Acad. de Stinte
Republ.
16. Absolute factorization of
matrices in the rings of
block-triangular matrices. (with
17. 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.
18. Seniscalar equivalence of polynomial matrices and the solutions of the Sylvester matrix polynomial equations. (with Dzhaliuk N.S). Mathematical bulletin of the Shevchenko scientific society. 9, 81–88, (2012).
19. Solutions of matrix polynomial diophantine equation (with Dzhaliuk N.S). Applied problems of mechanics and mathematics. 10, 55 – 61, (2012).
20. The matrix diophantine equations AX+ BY= C (with Dzhaliuk N.S). Carpathian Mathematical Publications 3 (2), 49–56, (2011).
21. Parallel factorizations of matrices over rings and their connections (with Dzhaliuk N.S). Applied problems of mechanics and mathematics. 8, 7 – 17, (2010).
22. On the stable range of matrix rings (with Zabavsky B.V.). Ukrainian Mathematical Journal 61 (11), 1853–1857, (2009).
23. On solvents of matrix polynomial equations and their number. Applied problems of mechanics and mathematics. 7, 52 – 56, (2009).
24. 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).
25. 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).
26. Multiplicities of characteristic roots, degrees of elementary divisors and factorization of polynomial matrices. Mat. Metody Fiz.-Mekh. Polya 48, (2), 7–17, (2005).
27. On solutions of matrix polynomial equations and the similarity of matrices. Mat. Metodi Fiz.-Mekh. Polya. 48, ( 4), 14–19, (2005).
28. 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).
29. Generalized equivalence of collections of matrices and common divisors of matrices. Algebra and Discrete Mathematics. 2, 84 – 91, (2004).
30. On common divisors of polynomial matrices (with Zelisko V.R.) . Applied problems of mechanics and mathematics. 2, 56 – 60, (2004).
31. On divisibility and factorization of matrices. Mat. Stud. 22, ( 2), 115-120 (2004).
32. Standard form of pairs of matrices with respect to generalized equivalence. Visnyk Lviv. Univ., Ser. Mech-Math. 61, 148 – 155, (2003).
33. Structure-theoretical properties of matrices finitely generated principal ideal rings (with Komarnytsky N.Ya.). Mat. Metody Fiz.-Mekh. Polya. 46, (2), 7 – 21, (2003).
34.
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).
35.
Generalized equivalence of pairs of matrices.
Linear and Multilinear Algebra. 48, (2), 179 – 188, (2000).
36.
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).
37.
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).
38.
Generalized equivalence of pairs of matrices. . Mat. Stud. 8, (2),
147 – 152, (1997).
39.
On the parallel
factorization of matrices over principal ideal rings Journal of Mathematical Sciences,
40.
Parallel factorizations of polynomial matrices. Ukrainian Mathematical Journal 44
(9), 1123–1127, (1992).
41.
Semiscalar equivalence and the
factorization of polynomial matrices Ukrainian Mathematical Journal. 42, (5),
570–574, (1990).
42. Decomposition of polynomial matrices into factors with prescribed canonical diagonal forms Journal of Soviet Mathematics. 64 (5), 1129–1131, (1993).
43. Semiscalar equivalence and the Smith normal form of polynomial matrices Journal of Soviet Mathematics. 66, No.1, 2030–2033, (1993).
44.
Factorization of polynomial matrices
over arbitrary fields. (with Prokip V.M.) Ukrainian Mathematical Journal. 38, (4), 409–412, (1986).
45. Cell-triangular and cell-diagonal factorizations of cell-triangular and cell-diagonal polynomial matrices. Mathematical Notes. 37, 431–435, (1985).
46.
Linear divisors and reducibility of
polynomial matrices. Ukrainian Mathematical Journal. 36,
(2) 176–181,
(1984).
47.
Problems of the factorization of matrix
polynomials. Mat.
Metody Fiz.-Mekh. Polya 14, 19–26, (1981).
48.
On the number of solutions of a matrix
equation. Mat. Metody Fiz.-Mekh. Polya 12, 56–58, (1980).
49.
Absolute expansibility of matrix polynomials Mat. Metody
Fiz.-Mekh. Polya 9, 37–41, (1979).
50. Decomposability of polynomial matrices into a product of linear factors (with Kazimirs' kii PS). Mat. Met. Fiz.-Mekh. Polya. 8, 3 – 9, (1978).
51. On the equivalence of polynomial matrices (with Kazimirs' kii PS). Theoretical and Applied Problems of Algebra and Differential Equations. 61 – 66, (1977).
Phone service: (032) 258 51 87
E-mail: vpetrych@iapmm.lviv.ua