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 …

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 …

A commutative Noetherian ring R is said to be Tor-persistent if, for any finitely generated R-
module M, the vanishing of Tor i R (M, M) for i≫ 0 implies M has finite projective dimension …

Let A be a finite dimensional algebra over field K and X a finitely generated A-module. X is
said to be reflexive (resp. torsionless) if the canonical map σ X: X→ X** is an isomorphism …

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 …

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 …

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

We study modules over a commutative artin local ring R. For the most part, we concentrate
on almost split sequences with uniserial modules in its end terms. Based on our …

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 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 …