On a classification of ideals of local rings for irreducible curve singularities

TL;DR

This paper introduces a systematic method for classifying ideals by codimension in local rings of irreducible curve singularities, addressing a specific algebraic classification challenge.

Contribution

The paper presents a new systematic approach to classify ideals in local rings of irreducible curve singularities by codimension, advancing algebraic understanding.

Findings

Developed a systematic classification method

Applied the method to local rings of irreducible curve singularities

Provided insights into the structure of ideals in these rings

Abstract

We consider a classification problem of ideals by codimension in case rings are the local rings of irreducible curve singularities. In this paper, we introduce a systematic method to solve this problem.