Decomposition of integrally closed ideals in Arf rings

TL;DR

This paper explores the structure of Arf rings by decomposing integrally closed ideals and analyzing their prime ideal structure, especially in local ring cases, advancing understanding of their algebraic properties.

Contribution

It introduces a decomposition method for integrally closed ideals in Arf rings and characterizes their prime ideal structure, particularly for local rings.

Findings

Decomposition of integrally closed ideals in Arf rings.

Prime ideal structure characterization in local Arf rings.

Structural insights into the integral closure of Arf rings.

Abstract

This study investigates the structure of Arf rings. From the perspective of ring extensions, a decomposition of integrally closed ideals is given. Using this, we present a kind of their prime ideal decomposition in Arf rings, and determine their structure in the case where both R and the integral closure of R are local rings.