\(P\)-clean rings. (Q884213)
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scientific article; zbMATH DE number 5164009
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(P\)-clean rings. |
scientific article; zbMATH DE number 5164009 |
Statements
\(P\)-clean rings. (English)
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13 June 2007
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Summary: We unify the structures of various clean rings by introducing the notion of \(P\)-clean rings. Some properties of \(P\)-clean rings are investigated, which generalize known results on clean rings, semiclean rings, \(n\)-clean rings, and so forth. By the way, we answer a question of \textit{G. Xiao} and \textit{W. Tong} [Commun. Algebra 33, No. 5, 1501-1517 (2005; Zbl 1080.16027)] on \(n\)-clean rings in the negative.
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\(P\)-clean rings
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generalized clean rings
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semiclean rings
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\(n\)-clean rings
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sums of units
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idempotents
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