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 …

The celebrated Auslander-Reiten Conjecture, on the vanishing of self extensions of a
module, is one of the longstanding conjectures in ring theory. Although it is still open, there …

This paper studies vanishing of Ext modules over Cohen–Macaulay local rings. The main
result of this paper implies that the Auslander–Reiten conjecture holds for maximal Cohen …

In this paper, sufficient conditions for finitely generated modules over a commutative
noetherian ring to be projective are given in terms of vanishing of Ext modules. One of the …

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 …

For a finitely generated module M over a commutative Noetherian ring R, we settle the
Auslander–Reiten conjecture when at least one of Hom R (M, R) and Hom R (M, M) has …

In this paper, we investigate the maximal Cohen–Macaulay property of tensor products of
modules, and then give criteria for projectivity of modules in terms of vanishing of Ext …

Let R be a noetherian commutative local ring, and M, N be finitely generated R-modules.
Then a generalized form of Serre's Vanishing conjecture can be stated as follows: if then …

We consider a dual notion of the famous Auslander-Reiten Conjecture in case of Noetherian
algebras over commutative Noetherian rings. Firstly, in the introduction, we will examine its …

This paper aims to provide several relations between Bass and Betti numbers of a given
module and its deficiency modules. Such relations and the tools used throughout allow us to …