In this paper we explore consequences of the vanishing of ${\rm Ext} $ for finitely generated
modules over a quasi-fiber product ring $ R $; that is, $ R $ is a local ring such that …

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 …

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 …

In this note we study trace ideals of canonical modules. Characterizations of the trace ideals
in terms of annihilators of certain Ext modules are given. We apply our results to study many …

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 …

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 …

In this article, we study the trace ideal of semidualizing modules. Also, we introduce two new
classes of rings, namely quasi nearly Gorenstein and weakly nearly Gorenstein, which are …

Over a commutative Noetherian ring, we show that Auslander-Reiten conjecture holds true
for the class of (finitely generated) modules whose dual has finite complete intersection …

The celebrated Auslander-Reiten Conjecture, on the vanishing of self extensions of a
module, is one of the longstanding conjectures in ring theory. Although it is still open, there …

We investigate symmetry in the vanishing of Ext for finitely generated modules over local
Gorenstein rings. In particular, we define a class of local Gorenstein rings, which we call AB …