Lattice theoretic properties of approximation ideals
报告题目(Title)：Lattice theoretic properties of approximation ideals
报告人(Speaker)：扶先辉 教授 (东北师范大学)
地点(Place)：后主楼1220报告厅
时间(Time)：2019年12月31日15:00-16:00
邀请人(Inviter)：刘玉明
报告摘要
In this talk, I will present some new progress on ideal approximation theory. It is proved that a finite intersection of special preenveloping ideals in an exact category (\mathcal{A};\mathcal{E}) is a special preenveloping ideal. Dually, a finite intersection of special precovering ideals is a special precovering ideal. If the exact category has exact coproducts, resp.,exact products, the results extends to infinite families of special preenveloping, resp., special precovering, ideals. This leads to an ideal version of Bongartz Lemma, which states that if a: A\to B is a morphism in \mathcal{A}, then the ideal a^{\perp} is special preenveloping. In contrast to the classical version, the Ideal Bongartz Lemma required only minimal assumptions, and so may be interpreted as the first step in the Eklof-Trlifaj Lemma. The Ideal Bongartz Lemma implies that the ideal cotorsion pair generated by a small ideal is complete. This is a joint work with I. Herzog, J.S. Hu, and H.Y. Zhu.
