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arXiv · 1908.10185

Powers of monomial ideals and the Ratliff-Rush operation

Oleksandra Gasanova
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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 $\mathbb K[x_1, \ldots, x_n]$ and $\mathbb K[[x_1, \ldots, x_n]]$. 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 $\mathfrak m$-primary ideal in a local ring $(R,m)$, then the Ratliff--Rush associated ideal $\tilde I$ is the unique largest ideal containing $I$ and having the same Hilbert polynomial as $I$.

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Oleksandra Gasanova. 2019-08-27. Powers of monomial ideals and the Ratliff-Rush operation. https://arxiv.org/abs/1908.10185

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