We establish a link between trace modules and rigidity in modules over Noetherian rings.
We identify classes of modules which must have self-extensions and use the theory of trace …

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 …

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 …

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 …

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 …

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 left noetherian ring, we establish a bijective correspondence between equivalence
classes of cotilting-modules which are not necessarily finitely generated, and torsion pairs …

We develop the theory of trace modules up to isomorphism and explore the relationship
between preenveloping classes of modules and the property of being a trace module …

We study characterizations of sincere modules, sincere silting modules and tilting modules
in terms of various vanishing conditions. Let R be a perfect ring and T be an R-module. It is …

We prove that the Auslander–Reiten conjecture holds for commutative standard graded
artinian algebras, in two situations: the first is under the assumption that the modules …