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math.RA2019
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…
math.RA2019
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…
math.RA2019
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…