2019
Том 71
№ 5

All Issues

Domsha O.V.

Articles: 2
Brief Communications (Ukrainian)

2-Simple ore domains of stable rank 1

Domsha O.V., Zabavskii B. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1436–1440

It is known that a simple Bézout domain is a domain of elementary divisors if and only if it is 2-simple. We prove that, over a 2-simple Ore domain of stable rank 1, an arbitrary matrix that is not a divisor of zero is equivalent to a canonical diagonal matrix.

Brief Communications (Ukrainian)

Block-diagonal reduction of matrices over an $n$-simple Bézout domain $(n ≥ 3)$

Domsha O.V., Zabavskii B. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 275–280

It is known that a simple Bézout domain is the domain of elementary divisors if and only if it is 2-simple. The block-diagonal reduction of matrices over an $n$ -simple Bézout domain $(n ≥ 3)$ is realized.