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Ratliff-Rush Monomial Ideals

Veronica Crispin Quiñonez
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Abstract

Let $I$ be a regular $\mathfrak m$-primary ideal in $(R,\mathfrak m,k)$. Then the Ratliff-Rush ideal associated to $I$ is denoted by $\bar I$ and is defined as the largest ideal containing $I$ with the same Hilbert polynomial as $I$. In this paper we present a method to compute Ratliff-Rush ideals for a certain class of monomial ideals in the rings $k[x,y]$ and $k[[x,y]]$. We find an upper bound for the Ratliff-Rush reduction number for an ideal in this class. Moreover, we establish some new characterizations of when all powers of $I$ are Ratliff-Rush.

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Veronica Crispin Quiñonez. 2006-08-10. Ratliff-Rush Monomial Ideals. https://doi.org/10.1090/conm%2F423

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