Séminaire Lotharingien de Combinatoire, 82B.80 (2019), 12 pp.
Powers of monomial ideals and the Ratliff-Rush operation
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 C[x1, ..., xn] and C[[x1, ..., xn]]. As an interesting application it leads to an algorithm to compute Ratliff-Rush ideals for 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.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
The following versions are available: