Consider a non-trivial fiber product $ R= S\times _kT $ of local rings $ S $, $ T $ with
common residue field $ k $. Given two finitely generated $ R $-modules $ M $ and $ N $, we …

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

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 …

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 …

Given finitely generated modules M and N over a local ring R, the tensor product M⊗ RN
typically has nonzero torsion. Indeed, the assumption that the tensor product is torsion-free …

In this paper, we investigate the finiteness of Ext-indices for certain ring extensions. In this
direction, we introduce some conjectures and discuss the relationships among them. We …

Let R be a local complete intersection ring and let M and N be nonzero finitely generated R-
modules. We employ Auslander's transpose in the study of the vanishing of Tor and obtain …

We show that for a finitely generated module M over a complete intersection R, the
vanishing of for a certain number of consecutive values of i starting at n forces the projective …

Throughout this paper R will be a commutative ring with one, and all R-modules will be
unitary. Our purpose is to study commutative ring exten-sions S of R. As a key tool in our …

Let A be an Artin algebra. As we know, the construction of the well-known Auslander-Reiten
sequence is based on the natural (A, A)-bimodule A and the induced transpose, where the …