报 告 人：黄兆泳（南京大学教授、博士生导师）
报告题目：Homological Dimensions Relative to Preresolving Subcategories II
报告时间：2021年04月17日下午15：30-16：20
报告地点：静远楼1508
主办单位：数学与统计学院、科学技术研究院
报告人简介：
黄兆泳，南京大学教授、博士生导师。主要从事同调代数和代数表示论领域的研究工作。在Isr J. Math., J. Algebra, Publ. Res. Inst. Math. Sci.等国际著名数学期刊发表论文20余篇。主持国家级科研项目6项。曾获江苏省数学杰出成就奖。
报告摘要：
Let $\mathscr{A}$ be an abelian category having enough projective and injective objects,and let $\mathscr{T}$ be an additive subcategory of $\mathscr{A}$ closed under direct summands. A known assertion is that in a short exact sequence in $\mathscr{A}$, the $\mathscr{T}$-projective(respectively, $\mathscr{T}$-injective) dimensions of any two terms can sometimes induce an upper bound of that of the third term by using the same comparison expressions. We show that if $\mathscr{T}$ contains all projective (respectively, injective) objects of $\mathscr{A}$, then the above assertion holds true if and only if $\mathscr{T}$ is resolving (respectively, coresolving).
As applications, we get that a left and right Noetherian ring $R$ is $n$-Gorenstein if and only if the Gorenstein projective (respectively, injective, flat) dimension of any left $R$-module is at most $n$. In addition, in several cases, for a subcategory $\mathscr{C}$ of $\mathscr{T}$,we show that the finitistic $\mathscr{C}$-projective and $\mathscr{T}$-projective dimensions of $\mathscr{A}$ are identical.
邀请人：张孝金，李志伟