5 papers · 1 filter
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…
-Euclidean domain and skew Laurent series rings
Oleh Romaniv, Andrij Sagan
In this paper we proved that if is right -Euclidean domain, then skew Laurent formal series ring is right -Euclidean domain. We also showed that if is a right -Euc…