Rings close to semiregular. (Q2890884)
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scientific article; zbMATH DE number 6045512
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rings close to semiregular. |
scientific article; zbMATH DE number 6045512 |
Statements
12 June 2012
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idempotent liftings
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semiregular rings
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unit-regular rings
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strongly \(\pi\)-regular rings
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Rings close to semiregular. (English)
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A ring \(R\) is called semiregular if \(R/J\) is regular and idempotents lift modulo the Jacobson radical \(J\) of \(R\). A ring is called semi (*)-regular if idempotents lift modulo \(J\), and \(R/J\) satisfies the property (*), where (*) is (one-sided) unit-regular or strongly regular or (unit, strongly, weakly) \(\pi\)-regular. The authors investigate all these properties, establishing various characterizations and giving some relevant examples.
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