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...

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Bibliographic Details
Published inarXiv.org
Main Authors Marjan Sheibani Abdolyousefi, Rahman Bahmani Sangesari, Chen, Huanyin
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 24.06.2015
Subjects
Matrix reduction
Rings (mathematics)
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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.
ISSN:2331-8422