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首师代数论坛系列报告(十六)

发布日期:2020-12-12点击量:

报告人:扶先辉 教授(东北师范大学)

题目:Approximating ideals in additive categories

时间:2020年12月16日(周三)14:00-15:00

腾讯会议ID:572 9813 7220

会议链接:https://meeting.tencent.com/s/ai2R9IurQ07o

摘要

The notion of an ideal torsion pair (I, J) is introduced for an additive category X with suitable conditions. It is shown that if (I, J) is an ideal torsion pair in X, then I is a precovering ideal if and only if the ideal J is preenveloping. When X is an extriangulated category, the notion of extension of ideals is defined. It is proved that the class of precovering (respectively, preenveloping) ideals is closed under sums, intersections, products and extensions and also satisfies many nice formulas. In the case when X is an abelian category, there is a bijective correspondence between complete ideal torsion pairs and preradicals of X. If (A, E) is a Frobenius exact category, the triangulated structure of the stable category of A is used to show that every precovering ideal of (A, E) is special precovering. This is jointly with Hong-Yu Zhu and I. Herzog.

报告人简介

扶先辉,东北师范大学数学与统计学院教授,博士生导师,研究方向为同调代数与K-理论。他与合作者在正合范畴中引入了理想余挠对的概念,建立了研究态射逼近现象的理想逼近理论。通过引入态射范畴的ME-正合结构这一全新的正合结构,系统地发展了这一理论,并将D. Benson和Ph.G. Gnacadja关于群的phantom数的部分工作推广到了凝聚环,进而解决了D. Benson和Ph.G. Gnacadja提出的关于群的phantom数上界的一个公开问题。研究成果发表于Adv. Math.、Proc. London Math. Soc.、J. Algebra、J Pure Appl. Algebra等国际著名数学期刊。现主持国家自然科学基金面上基金项目。


论坛组织者

童纪龙 唐 舜 陈红星

举办单位

首都师范大学 数学科学学院 交叉科学研究院