Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the
derived category D (Mod-R). We determine the simple objects in this heart and their injective …

Given a torsion pair t=(T, F) in a module category R-Mod we give necessary and sufficient
conditions for the associated Happel–Reiten–Smalø t-structure in D (R) to have a heart Ht …

We study the $ t $-structure induced by an $ n $-tilting module $ T $ in the derived category
$\mathcal {D}(R) $ of a ring $ R $. Our main objective is to determine when the heart of the …

Let TR be a 1-tilting module with tilting torsion pair (Gen T, F) in Mod-R. The following
conditions are proved to be equivalent:(1) T is pure projective;(2) Gen T is a definable …

In [5] Brenner-Butler first introduced the notion of a tilting module in a rather restrictive form,
and in [6] Happel-Ringel generalized their work and extensively developed the theory of …

In a compactly generated triangulated category, we introduce a class of tilting objects
satisfying a certain purity condition. We call these the decent tilting objects and show that the …

We study the behavior of direct limits in the heart of a t-structure. We prove that, for any
compactly generated t-structure in a triangulated category with coproducts, countable direct …

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 …

We relate the theory of envelopes and covers to tilting and cotilting theory, for (infinitely
generated) modules over arbitrary rings. Our main result characterizes tilting torsion classes …

For a commutative noetherian ring\(R\), we establish a bijection between the resolving
subcategories consisting of finitely generated\(R\)-modules of finite projective dimension …