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 …

Auslander-Reiten Conjecture for commutative Noetherian rings predicts that a finitely
generated module is projective when certain Ext-modules vanish. But what if those Ext …

Let R be an associative ring with identity. We establish that the generalized Auslander-
Reiten conjecture implies the Wakamatsu tilting conjecture. Furthermore, we prove that any …

In this paper we explore consequences of the vanishing of ${\rm Ext} $ for finitely generated
modules over a quasi-fiber product ring $ R $; that is, $ R $ is a local ring such that …

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 …

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 …

We study self-extensions of modules over symmetric artin algebras. We show that non-
projective modules with eventually vanishing self-extensions must lie in AR components of …

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 …

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to
and irreducible epimorphisms from finitely generated free modules over a noetherian local …

There are many homological dimensions which are closely related to ring theoretic
properties. The notion of a AB ring has been introduced by Huneke and Jorgensen. It has …