Motivated by a result of Araya, we extend the Auslander–Reiten duality theorem to Cohen–
Macaulay local rings. We also study the Auslander–Reiten conjecture, which is rooted in …

Abstract The Auslander-Reiten conjecture is a notorious open problem about the vanishing
of Ext modules. In a Cohen-Macaulay complete local ring R with a parameter ideal Q, the …

In this paper, we study when the kernel of a complete hereditary cotorsion pair is the additive
closure of a tilting module. Applications go in three directions. The first is to characterize …

The Auslander bound of a module can be thought of as a generalization of projective
dimension. We say that the Auslander bound of $ M $ is finite if for all finitely generated …

It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric
Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten …

Let (C, E, s) be an extriangulated category with a proper class ξ of E-triangles. We study
complete cohomology of objects in (C, E, s) by applying ξ-projective resolutions and ξ …

We study derived invariance through syzygy complexes. In particular, we prove that syzygy-
finite algebras and Igusa--Todorov algebras are invariant under derived equivalences …

In this note, it is shown that the validity of the Auslander–Reiten conjecture for a given d-
dimensional Cohen–Macaulay local ring R depends on its validity for all direct summands of …

Mathematische Zeitschrift Page 1 Math. Z. (2012) 272:431–441 DOI 10.1007/s00209-011-0941-4
Mathematische Zeitschrift Tilting complexes and Auslander–Reiten conjecture Jiaqun Wei …

On the Generalized Auslander–Reiten Conjecture under Certain Ring Extensions Page 1
Canad. Math. Bull. Vol. 58 (1), 2015 pp. 134–143 http://dx.doi.org/10.4153/CMB-2014-052-9 c …