2018
Том 70
№ 4

All Issues

Romaniv A. M.

Articles: 2
Brief Communications (Ukrainian)

Greatest common divisor of matrices one of which is a disappear matrix

Romaniv A. M., Shchedrik V. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 3. - pp. 425–430

We study the structure of the greatest common divisor of matrices one of which is a disappear matrix. In this connection, we indicate the Smith normal form and the transforming matrices of the left greatest common divisor.

Brief Communications (Ukrainian)

Elementary Reduction of Matrices over Right 2-Euclidean Rings

Romaniv A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1717 – 1721

We introduce a concept of noncommutative (right) 2-Euclidean ring. We prove that a 2-Euclidean ring is a right Hermite ring, a right Bezout ring, and a GE n -ring. It is shown that an arbitrary right unimodular string of length not less than 3 over a right Bezout ring of stable rank possesses an elementary diagonal reduction. We prove that a right Bezout ring of stable rank 1 is a right 2-Euclidean ring.