Cotilting modules and Gorenstein homological dimensions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908465686904832 |
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| author | Divaani-Aazar, Kamran Fallah, Ali Mahin Tousi, Massoud |
| author_facet | Divaani-Aazar, Kamran Fallah, Ali Mahin Tousi, Massoud |
| contents | For a dualizing module $D$ over a commutative Noetherian ring $R$ with identity, it is known that its Auslander class $\mathscr{A}_D\left(R\right)$ (respectively, Bass class $\mathscr{B}_D\left(R\right)$) is characterized as those $R$-modules with finite Gorenstein flat dimension (respectively, finite Gorenstein injective dimension). We establish an analogue of this result in the context of cotilting modules over general Noetherain rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cotilting modules and Gorenstein homological dimensions Divaani-Aazar, Kamran Fallah, Ali Mahin Tousi, Massoud Representation Theory 18E30, 16G99, 18G05, 18G35 For a dualizing module $D$ over a commutative Noetherian ring $R$ with identity, it is known that its Auslander class $\mathscr{A}_D\left(R\right)$ (respectively, Bass class $\mathscr{B}_D\left(R\right)$) is characterized as those $R$-modules with finite Gorenstein flat dimension (respectively, finite Gorenstein injective dimension). We establish an analogue of this result in the context of cotilting modules over general Noetherain rings. |
| title | Cotilting modules and Gorenstein homological dimensions |
| topic | Representation Theory 18E30, 16G99, 18G05, 18G35 |
| url | https://arxiv.org/abs/2407.06364 |