Given a torsion theory (Y, X) in an abelian category C, the reflector I: C→ X to the torsion-free
subcategory X induces a reflective factorisation system (E, M) on C. It was shown by A …

One of the main ingredients of a tilting theory, a generalization of Morita equivalence
betweenR-Mod andS-Mod that has evolved from the work of S. Brenner and MCR Butler …

Let R be a small preadditive category, viewed as a “ring with several objects.” A right R-
module is an additive functor from Rop to the category Ab of abelian groups. We show that …

Torsion theories for abelian categories have been introduced in the 1960's with the
motivation and purpose of unifying a common behavior observed for abelian groups …

We introduce a relativized notion of (semi) normalcy for categories that come equipped with
a proper stable factorization system, and we use radicals (in the sense of module theory) …

We revisit a construction of wide subcategories going back to work of Ingalls and Thomas.
To a torsion pair in the category $ R\operatorname {-}\operatorname {mod} $ of finitely …

All rings considered have non zero identity elements, are associative but non necessarily
commutative. All modules are unitary and are left modules over the ring in question. Let R be …

We study the notion (for categories of modules) dual to that of torsion radical and its
connections with projective modules. Torsion radicals in categories of modules have been …

In [R. Colpi, KR Fuller, Tilting objects in abelian categories and quasitilted rings, Trans.
Amer. Math. Soc., in press] tilting objects in an arbitrary abelian category H are introduced …

Throughout the following note R will denote an associative ring with unit element 1. We shall
denote by R-mod [resp. mod-R] the category of all unitary left [resp. right] R-modules …