Generalized stable rings and regularity. (Q2880072)
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scientific article; zbMATH DE number 6023021
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized stable rings and regularity. |
scientific article; zbMATH DE number 6023021 |
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12 April 2012
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generalized stable rings
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regular rings
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diagonal reductions
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stable range conditions
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units
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Generalized stable rings and regularity. (English)
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A ring \(R\) is called a generalized stable ring if \(aR+bR=R\) with \(a,b\in R\) implies that \(a+by\in K(R)\) for some \(y\in R\), where \(K(R)\) is the set of elements \(x\in R\) such that \(sxt=1\) for some \(s,t\in R\). The author proves that the generalized stable property is invariant under Morita contexts. It is also shown that many classes of square matrices over generalized stable rings admit a diagonal reduction.
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