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On the number of generators of powers of an ideal

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arxiv 1707.07302 v3 pith:VFXKIXYE submitted 2017-07-23 math.AC

Jürgen Herzog , Maryam Mohammadei Saem , Naser Zamani This is my paper · ORCID
classification math.AC
keywords idealgeneratorsnumberpowersboundscm-typedenotesheight
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abstract

We study the number of generators of ideals in regular rings and ask the question whether $\mu(I)<\mu(I^2)$ if $I$ is not a principal ideal, where $\mu(J)$ denotes the number of generators of an ideal $J$. We provide lower bounds for the number of generators for the powers of an ideal and also show that the CM-type of $I^2$ is $\geq 3$ if $I$ is a monomial ideal of height $n$ in $K[x_1,\ldots,x_n]$ and $n\geq 3$.

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  1. Powers of monomial ideals and the Ratliff-Rush operation

    math.AC 2019-08 conditional novelty 6.0 of 10

    For 'good' monomial ideals, the Ratliff-Rush closure equals the intersection of n ideals obtained by stabilizing along the coordinate axes.

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