When are the classes of Gorenstein modules (co)tilting?
For the class of Gorenstein projective (resp. injective and flat) modules, we investigate and settle the questions when the middle class is tilting and the other ones are cotilting. The applications have in three directions. The first is to obtain the coincidence between the 1-tilting and silting pr...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.639/ |
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| author | Wang, Junpeng Liu, Zhongkui Zhao, Renyu |
| author_facet | Wang, Junpeng Liu, Zhongkui Zhao, Renyu |
| author_sort | Wang, Junpeng |
| collection | DOAJ |
| description | For the class of Gorenstein projective (resp. injective and flat) modules, we investigate and settle the questions when the middle class is tilting and the other ones are cotilting. The applications have in three directions. The first is to obtain the coincidence between the 1-tilting and silting property, as well as the 1-cotilting and cosilting property of such classes respectively. The second is to characterize Gorenstein modules via finitely generated modules, which provides a proof of that left Noetherian rings with finite left Gorenstein global dimension satisfy First Finitistic Dimension Conjecture and a result related to a question posed by Bazzoni in [J. Algebra 320 (2008) 4281-4299]. The last is to give some new characterizations of Dedekind and Prüfer domains and commutative Gorenstein Artin algebras as well as general (possibly not commutative) Gorenstein rings and Ding–Chen rings. |
| format | Article |
| id | doaj-art-5ac68f2907484b12aa8cb55bd67115a5 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-5ac68f2907484b12aa8cb55bd67115a52025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111301132510.5802/crmath.63910.5802/crmath.639When are the classes of Gorenstein modules (co)tilting?Wang, Junpeng0Liu, Zhongkui1Zhao, Renyu2Department of Mathematics, Northwest Normal University, Lanzhou 730070, People’s Republic of ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, People’s Republic of ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, People’s Republic of ChinaFor the class of Gorenstein projective (resp. injective and flat) modules, we investigate and settle the questions when the middle class is tilting and the other ones are cotilting. The applications have in three directions. The first is to obtain the coincidence between the 1-tilting and silting property, as well as the 1-cotilting and cosilting property of such classes respectively. The second is to characterize Gorenstein modules via finitely generated modules, which provides a proof of that left Noetherian rings with finite left Gorenstein global dimension satisfy First Finitistic Dimension Conjecture and a result related to a question posed by Bazzoni in [J. Algebra 320 (2008) 4281-4299]. The last is to give some new characterizations of Dedekind and Prüfer domains and commutative Gorenstein Artin algebras as well as general (possibly not commutative) Gorenstein rings and Ding–Chen rings.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.639/Gorenstein projective (resp. injective and flat) module(co)tilting classfinitistic dimension conjecture(strongly) finite type |
| spellingShingle | Wang, Junpeng Liu, Zhongkui Zhao, Renyu When are the classes of Gorenstein modules (co)tilting? Comptes Rendus. Mathématique Gorenstein projective (resp. injective and flat) module (co)tilting class finitistic dimension conjecture (strongly) finite type |
| title | When are the classes of Gorenstein modules (co)tilting? |
| title_full | When are the classes of Gorenstein modules (co)tilting? |
| title_fullStr | When are the classes of Gorenstein modules (co)tilting? |
| title_full_unstemmed | When are the classes of Gorenstein modules (co)tilting? |
| title_short | When are the classes of Gorenstein modules (co)tilting? |
| title_sort | when are the classes of gorenstein modules co tilting |
| topic | Gorenstein projective (resp. injective and flat) module (co)tilting class finitistic dimension conjecture (strongly) finite type |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.639/ |
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