Powers of monomial ideals and the Ratliff–Rush operation. (May 2021) - Gasanova, Oleksandra
Abstract: Powers of (monomial) ideals is a subject that still calls attraction in various ways. In this paper we present a nice presentation of high powers of ideals in a certain class in K [ x 1, …, x n ] and K [ [ x 1, …, x n ] ] . As an interesting application it leads to an algorithm for computation of the Ratliff–Rush operation on ideals in that class. The Ratliff–Rush operation itself has several applications, for instance, if I is a regular m -primary ideal in a local ring ( R, m ), then the Ratliff–Rush associated ideal I ˜ is the unique largest ideal containing I with the same Hilbert polynomial as I .