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Elementary divisor rings with Dubrovin-Komarnytsky property

Victor Bovdi, Bohdan Zabavsky

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.

Elementary divisor rings with Dubrovin-Komarnytsky property

Abstract

We introduce noncommutative rings with -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 . 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.

Paper Structure

This paper contains 3 sections, 18 theorems, 34 equations.

Table of Contents

  1. Introduction
  2. Main Results and relations between them
  3. Proofs

Key Result

theorem 1

If $R$ is a Bézout ring of stable range $1$, then

Theorems & Definitions (35)

  • theorem 1
  • theorem 2
  • theorem 3
  • theorem 4
  • theorem 5
  • theorem 6
  • theorem 7
  • theorem 8
  • corollary 1
  • corollary 2
  • ...and 25 more