Abstract
Let Λ be an Artin algebra. In 2014, Adachi, Iyama, and Reiten proved that the torsion functorially finite classes in can be described by the τ-tilting theory. The aim of this paper is to introduce the notion of F-torsion class in
where F is an additive subfunctor of
and to characterize when these classes are preenveloping and F-preenveloping. In order to do that, we introduce the notion of F-presilting Λ-module. The latter is both a generalization of τ-rigid and F-tilting in
2020 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors are greatly indebted to the referee for his/her carefully reading and helpful suggestions.