AN ALGORITHM FOR COMPUTING THE RATLIFF–RUSH CLOSURE

Abstract

Let I ⊂ 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 Ĩ for the ideal I = 〈m0, …, mn〉 whenever mi is contained in the integral closure of the ideal 〈xan, yb0〉. This generalizes of the work of Crispin [2]. Also, it provides generalizations and answers for some questions given in [6], and enables us to construct infinite families of Ratliff–Rush ideals.