Francesca Fedele

Lattices of pretorsion classes

Since their introduction by Dickson, torsion theories have played a key role in the study of abelian categories. Recently, pretorsion theories have been introduced as a “non-pointed version” of torsion theories for general categories. After introducing this framework, in this talk we will investigate pretorsion classes in modA (the category of finitely generated modules over a finite dimensional k-algebra A) and study the lattice they form under inclusion. We will analyse when this lattice is distributive and compare it to the widely studied lattice of classic torsion classes in modA.
This is based on joint work with Federico Campanini and Emine Yıldırım.