Gorenstein $\mathrm{FP}_n$-flat modules and weak global dimensions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916507784577024 |
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| author | Becerril, Víctor |
| author_facet | Becerril, Víctor |
| contents | In this paper we characterize the relative Gorenstein weak global dimension of the generalized Gorenstein $\mathrm{FP}_n$-flat $R$-modules and Projective Coresolved $\mathrm{FP}_n$-flat $R$-modules recently studied by S. Estrada, A. Iacob, and M. A. Pérez. As application we prove that the weak global dimension that comes from the Gorenstein $\mathrm{FP}_n$-flat modules is finite over a Gorenstein $n$-coherent ring and coincide with the flat dimension of the right $\mathrm{FP}_n$-injective $R$-modules. This result extends the known for Gorenstein flat modules over Iwanaga-Gorenstein and Ding-Chen rings. We also show that there is a close relationship between the global dimensions of the generalized Gorenstein $\mathrm{FP}_n$-projectives and $\mathrm{FP}_n$-injectives and the relative Gorenstein weak global dimension presented here, obtaining in the process a balanced pair. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_12955 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gorenstein $\mathrm{FP}_n$-flat modules and weak global dimensions Becerril, Víctor Rings and Algebras Category Theory In this paper we characterize the relative Gorenstein weak global dimension of the generalized Gorenstein $\mathrm{FP}_n$-flat $R$-modules and Projective Coresolved $\mathrm{FP}_n$-flat $R$-modules recently studied by S. Estrada, A. Iacob, and M. A. Pérez. As application we prove that the weak global dimension that comes from the Gorenstein $\mathrm{FP}_n$-flat modules is finite over a Gorenstein $n$-coherent ring and coincide with the flat dimension of the right $\mathrm{FP}_n$-injective $R$-modules. This result extends the known for Gorenstein flat modules over Iwanaga-Gorenstein and Ding-Chen rings. We also show that there is a close relationship between the global dimensions of the generalized Gorenstein $\mathrm{FP}_n$-projectives and $\mathrm{FP}_n$-injectives and the relative Gorenstein weak global dimension presented here, obtaining in the process a balanced pair. |
| title | Gorenstein $\mathrm{FP}_n$-flat modules and weak global dimensions |
| topic | Rings and Algebras Category Theory |
| url | https://arxiv.org/abs/2303.12955 |