Let $ T $ be a tilting module. In this paper, Gorenstein $\pi [T] $-projective modules are
introduced and some of their basic properties are studied. Moreover, some characterizations …

This paper aims at generalizing the notions of “Auslander dual”,“k-torsionless” and “k-th
syzygy” modules to the relative setting with respect to a semidualizing module. It is shown …

In order to better unify the tilting theory and the Auslander–Reiten theory, Xi introduced a
general transpose called the relative transpose. Originating from this, we introduce and …

Recently, tilting and cotilting classes over commutative Noetherian rings have been
classified in [2]. We proceed and, for each n-cotilting class C, construct an n-cotilting module …

Given a good $ n $-tilting module $ T $ over a ring $ A $, let $ B $ be the endomorphism ring
of $ T $, it is an open question whether the kernel of the left-derived functor $ T\otimes^ L_B …

In the representation theory of algebras, the notion of a tilting module of finite projective
dimension (cf.[7]) is well known, and there are many papers concerning this. On the other …

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 …

Finally, let B and 8 be two rings, let 9 be a full subcategory of left R-modules closed under
direct sums and factor modules, let be a full subcategory of left S-modules containing ss and …

We introduce the notion of big tilting complexes over associative rings, which is a
simultaneous generalization of good tilting modules and tilting complexes over rings. Given …

Given any (faithful) quasi-progenerator RP, with endomorphism ring A End (RP), and any
tilting module AT, we prove that the module RV= RP AT is a (faithful)*-module, which is …