报告题目：Duality Pairs Induced by One-Sided Gorenstein Subcategories

报 告 人：黄兆泳 教授 南京大学

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邀 请 人：杨丹丹 李欢欢

报告时间：2020年11月14日（周六） 9：30-11：00

报告地点：腾讯会议:557344446

报告人简介：黄兆泳，南京大学数学系教授、博士生导师。主要从事代数表示论和同调代数相关课题的研究，已在Isr. J. Math.，J. Algebra，J. Pure Appl. Algebra等代数知名期刊上发表SCI论文90余篇。曾获中国高校科学技术奖自然科学奖二等奖和江苏省数学杰出成就奖；多次主持国家自然科学基金、教育部博士点基金和江苏省自然科学基金；应邀访问了日本、德国和美国十多所大学并作专题报告；多次应邀在国内外重要学术会议作大会报告。

报告摘要：For a ring $R$ and an additive subcategory $\mathcal{C}$ of the category ${\rm Mod}\;R$ of left $R$-modules, under some conditions we prove that the right Gorenstein subcategory of ${\rm Mod}\;R$ and the left Gorenstein subcategory of ${\rm Mod}\;R^{op}$ relative to $\mathcal{C}$ 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 ${\rm Mod}\;R$, where $\mathcal{G}\mathcal{F}_C(R)$ is the subcategory of ${\rm Mod}\;R$ consisting of $C$-Gorenstein flat modules and $\mathcal{G}\mathcal{I}_C(R^{op})$ is the subcategory of ${\rm Mod}\;R^{op}$ 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 ${\rm Mod}\;R^{op}$, where $\mathcal{A}_C(R^{op})$ is the Auslander class in ${\rm Mod}\;R^{op}$ and $l\mathcal{G}(\mathcal{F}_C(R))$ is the left Gorenstein subcategory of ${\rm Mod}\;R$ relative to $C$-flat modules.