### Reduction of matrices over Bezout rings and related problems of the theory of rings and modules

#### Speaker

### Andriy Gatalevych

Associate Professor

Faculty of Mechanics and Mathematics

Ivan Franko National University of Lviv

#### When & where:

**May 17, 2022 at 15 ^{00}, room 709**

**3-b Naukova Str., Lviv, Algebra Department**

Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of National Academy of Sciences of Ukraine

#### Abstract of talk

The report is devoted to the study of diagonal reduction of matrices over different classes of Bezout rings of finite stable range. In terms of K-theory, the conditions are indicated when an arbitrary commutative Bezout domain is an elementary divisor ring. Semihereditary Bezout rings of Gelfand range 1 are investigated. The known theorems for Bezout rings of finite Krull dimension are generalized. The results are also obtained for the case of noncommutative Bezout rings, which are related to the structural properties of the rings.

It has been proved that the commutative Bezout domain in which an arbitrary nonzero prime ideal is contained in the unique maximal ideal, is an elementary divisor ring. The notion of stable range indicates the conditions when an arbitrary commutative Bezout domain is an elementary divisor ring.

**Andriy Gatalevych**

May 17, 2022