Elementary matrix reduction over locally stable rings

A commutative ring R is locally stable provided that for any $a,b\in R$ such that $aR+bR=R$, there exist some $y\in R$ such that $R/(a+by)R$ has stable range 1.For a Bezout ring $R$, we prove that $R$ is an elementary divisor ring if and only if $R$ is locally stable if and only if $R$ has neat rang...

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Bibliographic Details
Main Authors Abdolyousefi, Marjan Sheibani, Sangesari, Rahman Bahmani, Chen, Huanyin
Format Journal Article
LanguageEnglish
Published 24.06.2015
Subjects
Mathematics - Rings and Algebras
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Summary:A commutative ring R is locally stable provided that for any $a,b\in R$ such that $aR+bR=R$, there exist some $y\in R$ such that $R/(a+by)R$ has stable range 1.For a Bezout ring $R$, we prove that $R$ is an elementary divisor ring if and only if $R$ is locally stable if and only if $R$ has neat range 1.
DOI:10.48550/arxiv.1506.07544