Trace does not preserve Reflexivity

2025/09/16 by Lindo, Haydee, Maitra, Sarasij, Zhang, William
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.12576

Abstract

In this note, we address a question raised in a recent work by Dao-Maitra-Sridhar, regarding the preservation of reflexivity under taking trace. We answer this question negatively. We also study a few cases where the question has a positive answer in a one dimensional, analytically unramified Cohen-Macaulay local ring.

Citations

• Annihilators of (co)homology and their influence on the trace Ideal
• Extremal behavior of reduced type of one dimensional rings
• Reflexive modules over the endomorphism algebras of reflexive trace ideals
• Partial Trace Ideals, Torsion and Canonical Module
• Reflexive modules over Arf local rings
• On reflexive and I-Ulrich modules over curve singularities
• Trace ideals, normalization chains, and endomorphism rings
• Rings whose ideals are isomorphic to trace ideals
• Correspondence between trace ideals and birational extensions with application to the analysis of the Gorenstein property of rings
• Trace Ideals and the Gorenstein Property
• Totally reflexive modules over rings that are close to Gorenstein
• Trace Ideals and Centers of Endomorphism Rings of Modules over\n Commutative Rings

Related

• Reflexivity revisited
• Independence of the total reflexivity conditions for modules
• Stable trace ideals and applications
• Upper bound on the colength of the trace of the canonical module in dimension one
• Integral closure of 1-dimensional rings