# Algebraický seminář

Current seminar: Tuesday, February 18th, 17:20 - 18:20, the seminar room of KA (319/334)

## Xianhui Fu (Northeast Normal Univ. Changchun, CLR):Infinite powers of approximating ideals

Abstract: In this talk, we present and prove an ideal version of Eklof's Lemma. After introducing the notion of the \alpha-th inductive power of a special preenveloping ideal for an ordinal \alpha, we show that the \alpha-th inductive power of a special preenveloping ideal is still special preenveloping for any ordinal \alpha. As applications, we prove that if $R$ is a right coherent ring and the class of pure projective right $R$-modules is closed under extensions, then every FP-projective module is pure projective; and show that in the derived category of modules over a ring $R$, the \aleph_0-th inductive power of the ghost ideal is zero. This talk is based on a joint work with Ivo Herzog, Sergio Estrada, and Sinem Odabasi.

Forthcoming:

24.2. - Edoardo Lanari (MU AVCR): Cartesian factorization systems and pointed cartesian fibrations of ∞-categories

2.3. - Jan Šaroch (MFF UK): TBA

Previous program:

The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.

Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.