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| Content Provider | Springer Nature Link |
|---|---|
| Author | Nishida, Kenji |
| Copyright Year | 2006 |
| Abstract | We generalize results of Foxby concerning a commutative Nötherian ring to a certain noncommutative Nötherian algebra Λ over a commutative Gorenstein complete local ring. We assume that Λ is a Cohen–Macaulay isolated singularity having a dualizing module. Then the same method as in the commutative cases works and we obtain a category equivalence between two subcategories of mod Λ, one of which includes all finitely generated modules of finite Gorenstein dimension. We give examples of such algebras which are not Gorenstien; orders related to almost Bass orders and some k-Gorenstein algebras for an integer k. |
| Ending Page | 31 |
| Page Count | 19 |
| Starting Page | 13 |
| File Format | |
| ISSN | 1386923X |
| e-ISSN | 15729079 |
| Journal | Algebras and Representation Theory |
| Issue Number | 1 |
| Volume Number | 9 |
| Language | English |
| Publisher | Springer Netherlands |
| Publisher Date | 2006-04-19 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Associative Rings and Algebras almost Bass order Gorenstein dimension Noetherian rings and modules Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) Non-associative Rings and Algebras dualizing module Commutative Rings and Algebras k-Gorenstein algebra Representations of orders, lattices, algebras over commutative rings Artinian rings and modules |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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