On Gorenstein rings (Q1096701)
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scientific article; zbMATH DE number 4031893
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Gorenstein rings |
scientific article; zbMATH DE number 4031893 |
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On Gorenstein rings (English)
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1988
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If R is noetherian, injective resolvents can be constructed. In this paper, it is shown that every injective resolvent \(...\to E_ 1\to E_ 0\to M\to 0\) is exact at \(E_ i\), \(i\geq n-1\), if and only if R is Gorenstein of dimension at most n. Additional characterizations of such rings are discussed. Finally, syzygies for injective resolvents are characterized in the case R is Gorenstein of dimension at most 1.
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noetherian ring
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Gorenstein ring
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injective dimension
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flat dimension
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injective resolvents
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syzygies
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