1 citations · 1 across the 10 of their papers we have counts for
12 papers
Rings of the right (left) almost stable range 1
Victor Bovdi, Bohdan Zabavsky
We introduce a concept of rings of right (left) almost stable range and we construct a theory of a canonical diagonal reduction of matrices over such rings. A description of ne…
Elementary divisor rings with Dubrovin-Komarnytsky property
Victor Bovdi, Bohdan Zabavsky
We introduce noncommutative rings with -property (Dubrovin-Komarnytsky's property) and investigate elementary divisor rings with such property. Mostly we pay attention to these…
Rings of simple range 2
Bohdan Zabavsky, Oleh Romaniv, Andrij Sagan
We introduce the concept of rings of simple range 2. Based on this concept, we build a theory diagonal reduction of matrices over Bezout domain. In particular we show that invarian…
Clear elements and clear rings
Bohdan Zabavsky, Olha Domsha, Oleh Romaniv
An element in a ring is called clear if it is the sum of unit-regular element and unit. An associative ring is clear if every its element is clear. In this paper we defined cle…
Reduction of matrices over simple Ore domains
Victor Bovdi, Bohdan Zabavsky
We study the theory of diagonal reductions of matrices over simple Ore domains of finite stable range. We cover the cases of 2-simple rings of stable range 1, Ore domains and certa…
Diagonal reduction of matrices over Bezout rings of stable range 1 with the Kazimirsky condition
Bohdan Zabavsky, Oleh Romaniv
We constuct the theory of diagonalizability for matrices over Bezout rings of stable range 1 with the Kazimirsky condition. It is shown that a ring of stable range 1 with the right…
Almost zip Bezout domain
Bohdan Zabavsky, Oleh Romaniv
J. Zelmanowitz introduced the concept of ring, which we call zip rings. In this paper we characterize a commutative Bezout domain whose finite homomorphic images are zip rings modu…
J-Noetherian Bezout domain which is not a ring of stable range 1
Bohdan Zabavsky, Oleh Romaniv
We proved that in J-Noetherian Bezout domain which is not a ring of stable range 1 exists a nonunit adequate element (element of almost stable range 1
A Bezout ring of stable range 2 which has square stable range 1
Bohdan Zabavsky, Oleh Romaniv
In this paper we introduced the concept of a ring of stable range 2 which has square stable range 1. We proved that a Hermitian ring which has (right) square stable range 1 is…
Diagonal reduction of matrices over commutative semihereditary Bezout rings
Bohdan Zabavsky, Andry Gatalevych
It is proven that every commutative semihereditary Bezout ring in which any regular element is Gelfand (adequate), is an elementary divisor ring.
Rings of Dyadic range 1
Bohdan Zabavsky
Using the concept of ring diadic range 1 we proved that a commutative Bezout ring is an elementary divisor ring iff it is a ring diadic range 1.
Type conditions of stable range for identification of qualitative generalized classes of rings
Bohdan Zabavsky
This article deals mostly with the following question: when is the classical ring of quotients of a commutative ring a ring of stable range 1? We introduce the concepts of a ring o…