Ratliff-Rush Monomial Ideals

Details Ratliff-Rush Monomial Ideals Ratliff-Rush Monomial Ideals

2006-08-10

arxiv.org/abs/math/0608261v1

Mathematics

Commutative Algebra

8 pages

Scientific paper

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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