We consider the bounded derived category D b (R mod) of a left Noetherian ring R. We give
a version of the Generalized Auslander–Reiten Condition for D b (R mod) that is equivalent …

Over a commutative noetherian ring $ R $, the prime spectrum controls, via the assignment
of support, the structure of both $\mathsf {Mod}(R) $ and $\mathsf {D}(R) $. We show that …

Let R be any ring. We motivate the study of a class of chain complexes of injective R-
modules that we call AC-injective complexes, showing that K (AC-Inj), the chain homotopy …

In this paper, we prove a version of Freyd's generating hypothesis for triangulated
categories: if D is a cocomplete triangulated category and S∈ D is an object whose …

In the setting of the unbounded derived category D(R) of a ring R of weak global dimension
at most one we consider t-structures with a definable coaisle. The t-structures among these …

We study the derived categories of small categories over commutative noetherian rings. Our
main result is a parametrization of the localizing subcategories in terms of the spectrum of …

Let R be a commutative noetherian ring. Denote by mod\, R mod R the category of finitely
generated R-modules. In this paper, we study n-torsionfree modules in the sense of …

The center $ Z (\mathcal {A}) $ of an abelian category $\mathcal {A} $ is the endomorphism
ring of the identity functor on that category. A localizing subcategory of a Grothendieck …

Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated
R-modules. In the present paper, we first provide various sufficient (and necessary) …

Let be a commutative noetherian ring. The notion of-wide subcategories of is introduced and
studied in Matsui–Nam–Takahashi–Tri–Yen in relation to the cohomological dimension of a …