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 …

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 …

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 …

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 …

The Nakayama conjecture is one of the most important conjectures in ring theory. The
Auslander-Reiten conjecture is closely related to it. The purpose of this paper is to show that …

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 …

Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of
cohomology of finitely generated modules. The failure of this conjecture—by a 2003 …

We give a principle in derived categories, which lies behind the classical Auslander–Reiten
duality and its generalized version by Iyama and Wemyss. We apply the principle to show …

arXiv:1710.01793v2 [math.AC] 13 Oct 2017 Page 1 arXiv:1710.01793v2 [math.AC] 13 Oct
2017 SELF-INJECTIVE COMMUTATIVE RINGS HAVE NO NONTRIVIAL RIGID IDEALS …

In this paper, we show that the Gorenstein global dimension of trivial ring extensions is often
infinite. Also we study the transfer of Gorenstein properties between a ring and its trivial ring …