2019
Том 71
№ 9

All Issues

Petrichkovich V. M.

Articles: 6
Brief Communications (Ukrainian)

On the stable range of matrix rings

Petrichkovich V. M., Zabavskii B. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 11. - pp. 1575-1578

It is shown that an adequate ring with nonzero Jacobson radical has a stable range 1. A class of matrices over an adequate ring with stable range 1 is indicated.

Brief Communications (Ukrainian)

A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations

Petrichkovich V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 6. - pp. 860–862

We establish that a pair A, B, of nonsingular matrices over a commutative domain R of principal ideals can be reduced to their canonical diagonal forms D A and D B by the common transformation of rows and separate transformations of columns. This means that there exist invertible matrices U, V A, and V B over R such that UAV a=DA and UAV B=DB if and only if the matrices B *A and D * B DA where B * 0 is the matrix adjoint to B, are equivalent.

Article (Ukrainian)

Parallel factorizations of polynomial matrices

Petrichkovich V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1228–1233

Conditions are established under which suggested factorizations of polynomial matrices over a field are parallel to factorizations of their canonical diagonal forms. An existence criterion of these factorizations of polynomial matrices is indicated and a method of constructing them is suggested.

Article (Ukrainian)

Semiscalar equivalence and the factorization of polynomial matrices

Petrichkovich V. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 5. - pp. 644–649

Article (Ukrainian)

Factorization of polynomial matrices over arbitrary fields

Petrichkovich V. M., Prokip V. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 478–483

Article (Ukrainian)

Linear divisors and reducibility of polynomial matrices

Petrichkovich V. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 2. - pp. 195 - 200