走向现代数学学术报告-扶先辉教授（No. 536）

报告题目：Lattice Theoretic Properties of Approximating Ideals

报告人：扶先辉 教授（东北师范大学）

报告时间：2022年10月21日 上午10:00

腾讯会议号：445-786-207

会议链接：https://meeting.tencent.com/dm/wKlEGnma9SCt

报告摘要：It is proved that a finite intersection of special preenveloping ideals in an exact category (A; E) is a special preenveloping ideal. Dually, a finite intersection of special precovering ideals is a special precovering ideal. A counterexample of Happel and Unger shows that the analogous state[1]ment about special preenveloping subcategories does not hold in classical approximation theory. If the exact category has exact coproducts, resp., exact products, these results extend to intersections of infinite families of special peenveloping, resp., special precovering, ideals. These techniques yield the Bongartz-Eklof-Trlifaj Lemma: if a: A→B is a morphism in A, then the ideal a⊥is special preenveloping. This is an ideal version of the Eklof-Trlifaj Lemma, but the proof is based on that of Bongartz’Lemma. The main consequence is that the ideal cotorsion pair generated by a small ideal is complete. This is joint work with Ivo Herzog, Jiangsheng Hu and Haiyan Zhu.

报告人简介：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。