An Algorithm for Computing the Ratliff-Rush Closure

TL;DR

This paper introduces an algorithm to compute the Ratliff-Rush closure of certain monomial ideals in two variables, generalizing previous work and enabling the construction of infinite families of such ideals.

Contribution

It presents a new algorithm for calculating Ratliff-Rush closures of specific monomial ideals, extending prior results and addressing open questions in the field.

Findings

Algorithm successfully computes Ratliff-Rush closures for targeted ideals.

Generalizes previous methods to broader classes of ideals.

Allows construction of infinite families of Ratliff-Rush ideals.

Abstract

Let I\subset K[x,y] be a <x,y>-primary monomial ideal where K is a field. This paper produces an algorithm for computing the Ratliff-Rush closure I for the ideal I=<m_0,...,m_{n}> whenever m_{i} is contained in the integral closure of the ideal <x^{a_{n}},y^{b_0}>. This generalizes of the work of Crispin \cite{Cri}. Also, it provides generalizations and answers for some questions given in \cite{HJLS}, and enables us to construct infinite families of Ratliff-Rush ideals.