We study torsion torsionfree (= TTF) triples in abelian and triangulated categories.(Notice
that TTF triples in a triangulated category are essentially in bijection with recollement data …

We introduce and study a new class of morphisms which includes morphisms represented
by monomorphisms in the sense of Auslander and Bridger. As an application, we give not …

Let R be a two-sided noetherian ring. Auslander and Bridger developed a theory of
projective stabilization of the category of finitely generated R-modules, which is called the …

We consider the equivalence from the stable module category to a subcategory $\mathcal
{L} _A $ of the homotopy category constructed by Kato. This equivalence induces a …

The stable module category has been realized as a subcategory of the unbounded
homotopy category of projective modules by Kato. We construct the triangulated hull of this …

A higher syzygy of a module with positive codimension is a maximal Cohen–Macaulay
module that plays an important role in Cohen–Macaulay approximation over Gorenstein …

In his work [26], SE Dickson defined the notion of torsion theory (now called torsion pair) in
the general framework of abelian categories, which generalizes the concept of …

We study when the stable category \mathcalA/⟨\mathcalT⟩ of an abelian category
\mathcalA modulo a full additive subcategory \mathcalT is balanced and, in case \mathcalT …

Under some strong cograde conditions, we obtain two different filtrations of modules in terms
of the properties of cotransposes of modules with respect to a semidualizing bimodule. Then …

We study when the stable category. 4/(T) of an abelian category. A modulo. a full additive
subcategory T is balanced and, in case T is functorially finite in. 4, we study a weak version …