On zero subrings and periodic subrings (Q1607755)
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scientific article; zbMATH DE number 1780279
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On zero subrings and periodic subrings |
scientific article; zbMATH DE number 1780279 |
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On zero subrings and periodic subrings (English)
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13 August 2002
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A ring \(R\) is an FZS-ring if every subring of \(R\) having trivial multiplication is finite. The author gives new proofs of two known results for FZS-rings and proves a result on periodic subrings. The known results for FZS-rings are: if \(R\) is nil then it is finite; if \(R\) is semiprime then it is a direct sum of a reduced ring and finitely many finite simple rings. The new result shows that a torsion ring \(R\) contains an infinite periodic subring if and only if \(R\) contains an infinite set of pairwise commuting periodic elements.
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FZS-rings
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periodic subrings
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nil rings
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semiprime rings
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direct sums
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reduced rings
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finite simple rings
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torsion rings
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pairwise commuting periodic elements
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0.7737389206886292
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0.7726365923881531
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