2019
Том 71
№ 11

All Issues

Gatalevych A. I.

Articles: 2
Brief Communications (Ukrainian)

Right Bézout ring with waist is a right Hermite ring

Gatalevych A. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 1. - pp. 136–138

We study noncommutative rings in which the Jacobson radical contains a completely prime ideal. It is proved that a right Bézout ring in which the Jacobson radical contains a completely prime ideal is a right Hermite ring. We describe a new class of Bézout rings that are not elementary divisor rings.

Brief Communications (Ukrainian)

On minimal prime ideals of commutative Bezout rings

Gatalevych A. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 1001–1005

We study the spectrum of minimal prime ideals of commutative Bezout rings. We apply the results obtained to the problem of diagonal reduction of matrices over rings of this sort.