报告题目：Higher Auslander-Solberg correspondence for Semi-primary rings
报告人： Mohammad Keshavarz 博士
主持人： Rasool Hafezi和张毅副 教授
报告时间：2026年9月29日（周二）10：30-11：30
报告地点：藕舫楼702室
报告摘要：In 1972, Ringel and Tachikawa generalized Auslander correspondence to semi-primary rings. Later, in 1974, Tachikawa showed that this generalization is in full generality and characterized rings whose projective modules form a Grothendieck category. This well-known result is called Ringel-Tachikawa's theorem and in this talk we will give a higher generalization of it. In fact, under some conditions, we will characterize rings whose modules with projective dimension less than a fixed positive integer form a Grothendieck category. We will also give a higher-Gorenstein generalization of Ringel-Tachikawa theorem and under some conditions will characterize rings whose modules with Gorenstein projective dimension less than a fixed positive integer form a Grothendieck category. The results shows that there is a close relationship between different objects in the theory of module categories, namely higher Auslander algebras, torsion theories, and Grothendieck categories. Some parts of the main results can also be considered as a generalization of Iyama's correspondence (well-known as higher Auslander correspondence) and Iyama-Solberg's correspondence (well-known as higher Auslander-Solberg correspondence) to left perfect and right coherent rings.
报告人简介：Dr Mohammad Keshavarz is a researcher in the representation theory of Artin algebras. He got his PhD from the University of Isfahan in 2017, and after that, he was a non-resident researcher at the Institute for Research in Fundamental Sciences (IPM) in Tehran from 2017 to 2021. He was also a postdoctoral researcher at East China Normal University from 2021 to 2024. Currently, he is a faculty member at Nantong University. He has published papers in J. Alg. Appl., Comm. Alg., J. Math. Soc. Japan, Bull. Sci. Math., and Sci. China Math.
欢迎广大师生参加。
数学与统计学院
江苏省应用数学（南京信息工程大学）中心
江苏省系统建模与数据分析国际合作联合实验室
2026年9月28日
