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 ideals to verify the Auslander–Reiten conjecture for syzygies of ideals over Artinian Gorenstein rings.
"On the nonrigidity of trace modules." J. Commut. Algebra 14 (2) 277 - 283, Summer 2022. https://doi.org/10.1216/jca.2022.14.277