Noncommutative elementary divisor rings
type: Item
instance of: scholarly article
title: Noncommutative elementary divisor rings
zbMATH Open document ID: 0642.16005
DOI: 10.1007/BF01060766
published in: Ukrainian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: The main results are the following: Theorem 7. Let R be a Bezout domain and for every finite set \(a_ 1,a_ 2,..\). of non-factorial elements of R there exist an \(a\in R\), such that \(aR=Ra\) and \(a_ i=af_ i\) for a factorial \(f_ i\). Then R is an elementary divisor domain. Theorem 8. Let R be a Bezout domain and for every \(a\in R\) such that \(aR=Ra\), there exists only finitely many maximal elements in the set of all 2-sided ideals lying in aR. Then R is an elementary divisor domain.
Mathematics Subject Classification ID: 16U80
Mathematics Subject Classification ID: 16Dxx
zbMATH DE Number: 4045933
zbMATH Keywords: Bezout domain
zbMATH Keywords: factorial elements
zbMATH Keywords: elementary divisor domain
zbMATH Keywords: 2-sided ideals
author: Bogdan Zabavskiy
MaRDI profile type: Publication
cites work: Elementary Divisors and Modules
cites work: Elementary Divisor Rings and Finitely Presented Modules
cites work: Commutative rings with restricted minimum condition
full work available at URL: https://doi.org/10.1007/bf01060766
OpenAlex ID: W2995347062
description: scientific article; zbMATH DE number 4045933