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, 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 …

The long-standing Auslander and Reiten Conjecture states that a finitely generated module
over a finite-dimensional algebra is projective if certain Ext-groups vanish. Several authors …

Two generalizations of Auslander-Reiten duality and applications Page 1 Two generalizations of
Auslander–Reiten duality and applications Arash Sadeghi and Ryo Takahashi …

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 $ R $ be a Noetherian local ring, and let $ C $ be a semidualizing $ R $-module. In this
paper, we present some results concerning to vanishing of $\operatorname {Ext} $ and finite …

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 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 …

VANISHING OF EXT MODULES OVER COHEN–MACAULAY RINGS 1. Introduction We refer
the reader to [10] (arXiv:2106.08583) for details Page 1 VANISHING OF EXT MODULES OVER …

We introduce the finitistic extension degree of a ring and investigate rings for which it is
finite. The Auslander–Reiten Conjecture is proved for rings of finite finitistic extension …