报告人：扶先辉教授（东北师范大学）

报告题目：Infinite powers of approximating ideals

报告时间：12月10日10：30-11：20            腾讯会议：366 530 021

摘要：Let (A,E) be an exact category such that each continuous system in (A,E) has colimits. In this talk, a theory of infinite powers of approximating ideals in the exact category (Arr(A), ME) is presented. A special case of the morphism version of Eklof's Lemma states that if J is an ideal, and a is an arrow which is $\mu$-${^{\perp}J}$-filtered in (Arr(A), ME), then a belongs to ${^{\perp}(J^{(\mu)})}$ . This is used to show that if J is a special preenveloping ideal with $\Omega^{-1}{(\mathcal{J})}$ a cosyzygy ideal of J, and if ${\Omega^{-1}_{\mu}(\mathcal{J})}$ is the class consisting of arrows $\mu$-filtered by $\Omega^{-1}(\mathcal{J})$ in (Arr(A),ME), then $J^{(\mu)}$ is a special preenveloping ideal with ${\Omega^{-1}_{\mu}(\mathcal{J})}$ a $\mathcal{J}^{(\mu)}$-cosyzygy ideal. This theory is used to study Generalized Generating Hypothesis. In particular, (1) it is used to show a dual of a result of Xu:  if the class of pure projective right R-modules is closed under extensions, then every FP-projective right R-module is pure projective; and (2) it is used to study the ghost ideal in the category of complexes. This talk is based on an ongoing project with S. Estrada, I. Herzog, and S. Odabasi.

个人简介：扶先辉，东北师范大学数学与统计学院副院长，教授，博士生导师，研究方向为同调代数与K-理论。研究论文发表于Adv. Math.，Proc. Lond. Math. Soc.，J. Algebra，J. Pure Appl. Algebra等权威数学杂志。主持国家自然科学基金项目4项，其中面上项目2项。