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

Key Points

• The aim is to characterize different types of one-dimensional Cohen-Macaulay local rings based on their reflexive ideals.
• Analyzed reflexive ideals in one-dimensional Cohen-Macaulay local rings.
• Investigated relationships between reflexive fractional ideals and the structure of the rings.
• Identified specific classes such as almost Gorenstein rings and Arf rings.
• Established characterizations for almost Gorenstein rings.
• Provided insights into rings with minimal multiplicity.
• Characterized the structural properties of Arf rings through their reflexive ideals.