9 papers
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…