Some classes of one-dimensional rings characterized by their reflexive ideals

2025/06/16 by Campochiaro, Pietro, D'Anna, Marco, Strazzanti, Francesco
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.13591

Abstract

We study reflexive ideals in one-dimensional Cohen-Macaulay local rings, providing characterizations of almost Gorenstein rings, rings with minimal multiplicity, and Arf rings, which describe their reflexive fractional ideals.

Citations

• The set of trace ideals of curve singularities
• Reflexive modules over Arf local rings
• On reflexive and I-Ulrich modules over curve singularities
• When is \mathfrakm:\mathfrakm an almost Gorenstein ring?
• Syzygies of Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings
• Almost Gorenstein rings - towards a theory of higher dimension -
• Almost Gorenstein rings
• Integral closure of ideals and annihilators of homology

Related

• Rings with canonical reduction
• Almost Gorenstein rings - towards a theory of higher dimension -
• Reflexive modules over Arf local rings
• Reflexive modules over the endomorphism algebras of reflexive trace ideals
• Integral closure of 1-dimensional rings