Suppose R is a commutative Noeheian ring with maximal ideal P and E is the injective hull
of R/P. The hereditary torsion theory associated with P has E has as an injective cogenerator …

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 …

Contravariantly finite subcategories have been useful in differentaspects of representation
theory (Auslander and Reiten, 1989, 1991; Auslander and Smalø, 1981) and they appear …

This paper settles a problem raised at the end of the seventies by JL Alperin [All], EC Dade
[Da] and JF Carlson [Cal], namely the classification of torsion endo-trivial modules for a finite …

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 …

For a hereditary torsion theory τ, a module A is called τ-completedly decomposable if it is a
direct sum of modules that are the τ-injective hull of each of their non-zero submodules. We …

Lemma 1.1 Let M be a left R-module, N a Jd XI-module, and f (Xi an element of R [XI. In a
natural way M@ ISJ isa left R [XI-module, so left mltiplication by fix) gives a NX1-linear …

Let α and β be automorphisms on a ring R and δ: R→ R an (α, β)-derivation. It is shown that
if F is a right Gabriel filter on R then F is δ-invariant if it is both α and β-invariant. A …

Suppose that R is a ring and that A is a chain complex over R. Inside the derived category of
differential graded R-modules there are naturally defined subcategories of A-torsion objects …