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 …

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 …

Given two ringsRandS, we study the category equivalences T⇄ Y, where T is a torsion class
ofR-modules and Y is a torsion-free class ofS-modules. These equivalences correspond to …

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 …

An important result in tilting theory states that a class of modules over a ring is a tilting class
if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective …

Let T be an infinitely generated tilting module of projective dimension at most one over an
arbitrary associative ring A, and let B be the endomorphism ring of T. We prove that if T is …

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 …

Let R be a ring and T an (infinitely generated) tilting module. Then T is of countable type; that
is, there is a set, 𝒞, of modules possessing a projective resolution consisting of countably …

Let R be a ring and P be an (infinite dimensional) partial tilting module. We show that the
perpendicular category of P is equivalent to the full module category Mod-S where S= End …