Canan Özeren, Dokuz Eylül University. Date: 03rd of May, 2023, Wednesday, Time: 10:30 – 12:00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206 (Online-Sakai-Graduate Meetings).
Abstract: We talk about the existence and uniqueness (up to isomorphism) torsion-free covers of modules over an integral domain (see [1]). We show that the classical definition of torsion-free cover and the definition of an 
-cover, where is the class of the torsion-free modules, coincide.
References
[1] E. Enochs: Torsion-free covering modules. (1963)
of an abelian group is defined in [2] as the group of 
s.t. 
and is denoted by 
. 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 
. We talk about the necessary and sufficient conditions for coGalois group, associated to a torsion free-cover of an object in 
to be trivial.
References
[1] E. Enochs: Torsion-free covering modules. (1963)
[2] E. Enochs, J. R. García 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 Dukun, Phd Thesis
[5] Molly Dukun, Phd Thesis