论文标题
双向戈伦斯坦子类别引起的二元性对
Duality Pairs Induced by One-Sided Gorenstein Subcategories
论文作者
论文摘要
对于环$ r $和一个添加子类别$ \ c $ of类别的$ \ mod r $，左$ r $ - 模块的mod r $，在某些情况下，我们证明$ \ mod r $的右Gorenstein子类别和左Gorenstein子类别的$ \ mod r^r^{op r^{OP} $ coprod a coprod a coprod a coprod a coprod a coprod coprod。令$ r，s $为戒指，每半间歇式化（$ r，s $） - bimodule。作为上述结果的应用，我们会知道，如果$ s $是正确的连贯性并且$ c $忠实地半单词化，则$（\ Mathcal {gf} _c（r），\ Mathcal {gi} _c（r^{op}） $ \ mod r $，其中$ \ MATHCAL {G} \ MATHCAL {f} _C（r）$是由$ \ mod r $组成的子类别，由$ c $ -gorenstein flat flat flat模块和$ \ mathcal {g} r^{op} $由$ c $ -gorenstein Injective模块组成； 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在$ \ mod r^{op} $中进行预先开发，其中$ \ Mathcal {a} _c（r^{op}）$是$ \ mod r^{op r^{op r^{op l \ natcal {g}（\ natcal {f} _c（f} _c（r）$ subore的$ r^{op r^{op r^{op r^{op l \ mathcal {g}） $ C $ -FLAT模块。
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.
