| Autor: |
Song, Weiling, Zhao, Tiwei, Huang, Zhaoyong |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Bulletin of the Malaysian Mathematical Sciences Society, 43(2) (2020), 1989--2007 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s40840-019-00786-w |
| Popis: |
For a ring $R$ and an additive subcategory $\C$ of the category $\Mod R$ of left $R$-modules, under some conditions we prove that the right Gorenstein subcategory of $\Mod R$ and the left Gorenstein subcategory of $\Mod R^{op}$ relative to $\C$ form a coproduct-closed duality pair. Let $R,S$ be rings and $C$ a semidualizing ($R,S$)-bimodule. As applications of the above result, we get that if $S$ is right coherent and $C$ is faithfully semidualizing, then $(\mathcal{GF}_C(R),\mathcal{GI}_C(R^{op}))$ is a coproduct-closed duality pair and $\mathcal{GF}_C(R)$ is covering in $\Mod R$, where $\mathcal{G}\mathcal{F}_C(R)$ is the subcategory of $\Mod R$ consisting of $C$-Gorenstein flat modules and $\mathcal{G}\mathcal{I}_C(R^{op})$ is the subcategory of $\Mod R^{op}$ consisting of $C$-Gorenstein injective modules; we also get that if $S$ is right coherent, then $(\mathcal{A}_C(R^{op}),l\mathcal{G}(\mathcal{F}_C(R)))$ is a coproduct-closed and product-closed duality pair and $\mathcal{A}_C(R^{op})$ is covering and preenveloping in $\Mod R^{op}$, where $\mathcal{A}_C(R^{op})$ is the Auslander class in $\Mod R^{op}$ and $l\mathcal{G}(\mathcal{F}_C(R))$ is the left Gorenstein subcategory of $\Mod R$ relative to $C$-flat modules. |
| Databáze: |
arXiv |
| Externí odkaz: |
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