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 Moldova Matematica. 76 (3), 3848, (2014).

3.     Absolute factorization of matrices in the rings of block-triangular matrices (with Dzhaliuk N.S.). Applied problems of mechanics and mathematics.. 11, 36 40, (2013).

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, 8188, (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), 4956, (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), 18531857, (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, 7989, (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), 717, (2005).

14.  On solutions of matrix polynomial equations and the similarity of matrices. Mat. Metodi Fiz.-Mekh. Polya. 48, ( 4), 1419, (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), 963965, (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, New York, 96, (2), 30223025, (1999).

27.   Parallel factorizations of polynomial matrices. Ukrainian Mathematical Journal 44 (9), 11231127, (1992).

28.   Semiscalar equivalence and the factorization of polynomial matrices Ukrainian Mathematical Journal. 42,  (5), 570574, (1990).

29.  Decomposition of polynomial matrices into factors with prescribed canonical diagonal forms Journal of Soviet Mathematics.  64 (5), 11291131, (1993).

30.  Semiscalar equivalence and the Smith normal form of polynomial matrices Journal of Soviet Mathematics. 66, No.1, 20302033, (1993).

31.  Factorization of polynomial matrices over arbitrary fields. (with Prokip V.M.) Ukrainian Mathematical Journal. 38, (4), 409412, (1986).

32.  Cell-triangular and cell-diagonal factorizations of cell-triangular and cell-diagonal polynomial matrices. Mathematical Notes. 37, 431435, (1985).

33.  Linear divisors and reducibility of polynomial matrices. Ukrainian Mathematical Journal. 36, (2) 176181,  (1984).

34.  Problems of the factorization of matrix polynomials. Mat. Metody Fiz.-Mekh. Polya 14, 1926, (1981).

35.  On the number of solutions of a matrix equation. Mat. Metody Fiz.-Mekh. Polya 12, 5658, (1980).

36.  Absolute expansibility of matrix polynomials Mat. Metody Fiz.-Mekh. Polya 9, 3741, (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