Séminaire Lotharingien de Combinatoire, 82B.80 (2019), 12 pp.

Oleksandra Gasanova

Powers of monomial ideals and the Ratliff-Rush operation

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 C[x₁, ..., x_n] and C[[x₁, ..., x_n]]. 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.

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