Artinian quotient rings of filtered rings (Q1320261)
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scientific article; zbMATH DE number 554272
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Artinian quotient rings of filtered rings |
scientific article; zbMATH DE number 554272 |
Statements
Artinian quotient rings of filtered rings (English)
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19 April 1994
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Let \(R\) be a noetherian ring with a regular normal element \(x\) satisfying \(\cap x^ i R = 0\). If \(R/xR\) has an artinian ring of quotients then so does \(R\). As application it is proved that \(R\) has an artinian ring of quotients if \(R\) is a right Zariski ring and the associated graded ring \(G(R)\) has an artinian ring of quotients.
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filtered rings
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noetherian ring
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artinian ring of quotients
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right Zariski ring
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graded ring
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