On the nonrigidity of trace modules

Haydee Lindo

doi:10.1216/jca.2022.14.277

Abstract

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.

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Haydee Lindo. "On the nonrigidity of trace modules." J. Commut. Algebra 14 (2) 277 - 283, Summer 2022. https://doi.org/10.1216/jca.2022.14.277

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Received: 5 April 2018; Revised: 15 September 2019; Accepted: 28 September 2019; Published: Summer 2022

First available in Project Euclid: 14 July 2022

MathSciNet: MR4452661

zbMATH: 1496.13014

Digital Object Identifier: 10.1216/jca.2022.14.277

Subjects:

Primary: 13C13 , 13D07 , 16E30

Keywords: Auslander–Reiten conjecture , Gorenstein ring , rigid module , trace ideal , trace module , vanishing of Ext

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