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In commutative algebra, a Gorenstein local ring is a commutative Noetherian local ring R with finite injective dimension as an R-module. There are many equivalent conditions, some of them listed below, often saying that a Gorenstein ring is self-dual in some sense.
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gorenstein ring local dimension rings noetherian commutative mr r-module space mathematics algebra finite duality macaulay doi serre k-vector field graded
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Gorenstein ring | is a | commutative Noetherian ring such that each localization at a prime ideal is a Gorenstein local ring | 0.90 | text |
| Gorenstein ring | related to Definitions | Gorenstein | 0.60 | section |
| Gorenstein ring | related to Definitions | Noetherian | 0.60 | section |
| Gorenstein ring | related to Definitions | Cohen | 0.60 | section |
| Gorenstein ring | related to Definitions | Macaulay | 0.60 | section |
| Gorenstein ring | related to Definitions | One | 0.60 | section |
| Gorenstein ring | related to Definitions | R-module | 0.60 | section |
| Gorenstein ring | related to Definitions | HomR | 0.60 | section |
| Gorenstein ring | related to Definitions | Equivalently | 0.60 | section |
| Gorenstein ring | related to Definitions | More | 0.60 | section |
| Gorenstein ring | related to Examples | Every | 0.60 | section |
| Gorenstein ring | related to Examples | Gorenstein | 0.60 | section |
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