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

TL;DR

This paper investigates reflexive ideals in one-dimensional Cohen-Macaulay local rings, offering characterizations of special classes like almost Gorenstein, minimal multiplicity, and Arf rings based on their reflexive fractional ideals.

Contribution

It provides new characterizations of these classes of rings through their reflexive fractional ideals, enhancing understanding of their structure.

Findings

Characterization of almost Gorenstein rings via reflexive ideals

Identification of rings with minimal multiplicity using reflexive ideals

Description of Arf rings through their reflexive fractional ideals

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.