Elementary divisor rings with Dubrovin-Komarnytsky property

2025/08/23 by Bovdi, Victor, Zabavsky, Bohdan · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.17100

Abstract

We introduce noncommutative rings with DK-property (Dubrovin-Komarnytsky's property) and investigate elementary divisor rings with such property. Mostly we pay attention to these kinds of noncommutative rings which have stable range 1. A theory of reduction matrices over such rings is constructed. As a consequence, new families of non-commutative rings of elementary divisor rings are constructed.

Citations

• Rings of the right (left) almost stable range 1
• Rosenbrock's Theorem on System Matrices over Elementary Divisor Domains
• Matrix invertible extensions over commutative rings. Part I: general theory
• On matrix invertible extensions over commutative rings
• Reduction of matrices over simple Ore domains
• Commutative Bezout domains of stable range 1.5
• Diagonal reduction of matrices over commutative semihereditary Bezout\n rings
• Elementary matrix reduction over Bezout duo rings

Cited by

• Rings of the right (left) almost stable range 1

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• Rings of the right (left) almost stable range 1
• Elementary Matrix Reduction Over Certain Rings
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• Diagonal reduction of matrices over Bezout rings of stable range 1 with the Kazimirsky condition