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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**[*x*_{1}, ..., *x*_{n}] and **C**[[*x*_{1}, ..., *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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