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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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Marjan Sheibani Abdolyousefi Chen, Huanyin Rahman Bahmani Sangesari |
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| Snippet | 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... |
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| Title | Elementary matrix reduction over locally stable rings |
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