Seminar “An overview on pretorsion theories", Algebra Seminar VUB, Bruxelles, Belgium.

Abstract: Pretorsion theories are defined as "non-pointed torsion theories", where the zero object and the zero morphisms are replaced by a class of "trivial" objects and a suitable ideal of morphisms respectively. Thus, the notion of pretorsion theory can be defined in any arbitrary category C, starting from a pair (T ,F) of full replete subcategories of C where T and F consist of the classes of "torsion" and "torsion-free" objects, and whose intersection defines the class of "trivial objects". In this talk, we shall present an overview on torsion and pretorsion theories, describing several examples in category theory and representation theory. Based on joint works with F. Borceux, M. Gran, W. Tholen, F. Fedele and E. Yıldırım.