Let be a commutative noetherian local ring of Krull dimension. We prove that the
cohomology annihilator of contains a power of if and only if, for some the th syzygies in are …

Let Λ be a Noetherian algebra and T∈ Λ-mod be an n-tilting module with Γ= End Λ (T). Then
Λ satisfies Auslander–Reiten conjecture if and only if so does Γ. As a consequence, we …

Vanishing of Ext modules over algebras | Archiv der Mathematik Skip to main content
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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 …

Let R be a Cohen-Macaulay local ring of dimension d with canonical module ωR. In this
article we extend Auslander-Reiten duality theorem to certain R-algebras. As a …

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 …

On the vanishing of self extensions over algebras | Archiv der Mathematik Skip to main content
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This paper studies the vanishing of $ Ext $ modules over group rings. Let $ R $ be a
commutative noetherian ring and $ ga $ a group. We provide a criterion under which the …

In this paper, we introduce the notion of excellent extensions of rings. Let Γ be an excellent
extension of an Artin algebra Λ, we prove that Λ satisfies the Gorenstein symmetry …

PROGRESS ON THE AUSLANDER–REITEN CONJECTURE Page 1 Bull. Aust. Math. Soc.
93 (2016), 433–440 doi:10.1017/S0004972716000071 PROGRESS ON THE AUSLANDER–REITEN …