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Gorenstein Analogue of Auslander's Theorem on the Global Dimension |
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| Authors: | Driss Bennis Kui Hu Fanggui Wang |
| Affiliation: | 1. Department of Mathematics, Laboratory of Analysis, Algebra, and Decision Support, Faculty of Science , Mohammed V-Agdal University , Rabat , Morocco d.bennis@fsr.ac.ma;4. driss_bennis@hotmail.com;5. College of Science , Southwest University of Science and Technology , Mianyang , China;6. College of Mathematics and Software Science , Sichuan Normal University , Chengdu , China |
| Abstract: | In this paper, we prove that the Gorenstein analogue of the well-known Auslander's theorem on the global dimension holds true. Namely, we prove that the Gorenstein global dimension of a commutative ring R is equal to the supremum of the set of Gorenstein projective dimensions of all cyclic R-modules. |
| Keywords: | Gorenstein global dimension of rings Gorenstein projective and injective dimensions of modules n-Gorenstein rings |