Gr-coherency of polynomial rings and \(G\)-graded rings (Q1964668)
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scientific article; zbMATH DE number 1406299
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gr-coherency of polynomial rings and \(G\)-graded rings |
scientific article; zbMATH DE number 1406299 |
Statements
Gr-coherency of polynomial rings and \(G\)-graded rings (English)
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9 April 2000
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Let \(R\) be a ring with identity. The authors prove that the polynomial ring \(R[T]\) is gr-coherent when regarded as a \(\mathbb{Z}\)-graded ring if and only if \(R\) is coherent. Also it is proved that a ring \(R\) graded by a finite group is gr-coherent if and only if \(R\) is coherent.
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graded rings
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polynomial rings
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graded coherent rings
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