Torsion Free Covers of Line Quivers

Canan Özeren, Dokuz Eylül University. Date: 6th of December, 2023, Wednesday, Time: 13.30 – 14.30. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206 (Online-Sakai-Graduate Meetings).

Abstract: Torsion-free covers exist for abelian groups (see [1]). The coGalois group of automorphisms a torsion-free cover \phi: T \rightarrow A of an abelian group A is defined in [2] as the group of f: T \rightarrow T s.t. \phi f= \phi and is denoted by G(\phi). The abelian groups for which the coGalois group is trivial were characterized in [3]. The notion of coGalois group can be defined in any category where we have a covering class. In [4], coGalois groups have been studied in the category of representations of the quiver q_2 : \cdot \rightarrow \cdot . We talk about the existence and uniqueness of the torsion free-cover of an object in (q_n, Z-mod) (see [5]).


[1] E. Enochs: Torsion-free covering modules. (1963).

[2] E. Enochs, J. R. Rozas and L. Oyonarte: Compact coGalois groups. (2000).

[3] E. Enochs and J. Rada: Abelian groups which have trivial absolute \\ coGalois group. (2005).

[4] Paul Hill, Abelian group pairs having a trivial coGalois Group. (2006).

[5] Molly Dunkum Wesley, Phd Thesis at The Graduate School University of Kentucky. (2005)