On rings whose primitive factor rings are left Artinian (Q5943059)
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scientific article; zbMATH DE number 1642148
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On rings whose primitive factor rings are left Artinian |
scientific article; zbMATH DE number 1642148 |
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On rings whose primitive factor rings are left Artinian (English)
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28 October 2001
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The authors prove that if \(R\) is a Min-E ring, then the following statements are equivalent: (1) Every left primitive factor ring of \(R\) is left Artinian; (2) \(R\) is a \(\pi\)-regular ring; (3) \(R\) is an exchange ring; (4) \(R\) is a clean ring. Further, they obtain other related results on Min-E rings without an infinite set of orthogonal idempotents.
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left primitive factor rings
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left Artinian rings
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\(\pi\)-regular rings
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exchange rings
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clean rings
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idempotents
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