Exchange rings satisfying unit 1-stable range (Q2769864)
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scientific article; zbMATH DE number 1702070
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Exchange rings satisfying unit 1-stable range |
scientific article; zbMATH DE number 1702070 |
Statements
2 December 2002
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primitive factors
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primitive ideals
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exchange rings
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unit 1-stable ranges
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strongly \(\pi\)-regular rings
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Exchange rings satisfying unit 1-stable range (English)
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Let \(R\) have all primitive factors Artinian, i.e., \(R/P\) is Artinian for every primitive ideal \(P\) of \(R\). The author gives a necessary and sufficient condition under which every exchange ring with primitive factors Artinian satisfies unit 1-stable range. In addition, a new elementwise characterization of strongly \(\pi\)-regular rings is obtained.
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