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arXiv · 1810.05896

The $*$-core of the graded maximal ideal in a Stanley-Reisner ring

Thomas M. Ales
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Abstract

We consider ideals $I$ in a Stanley-Reisner ring $k[\Delta]$ over the simplical complex $\Delta$, such that the tight closure of $I$, $I^*$, is equal to $\mathfrak{m}$, the standard graded maximal ideal of $k[\Delta]$. We determine the minimal number of generators of $I$ to be the $\dim \Delta+1$ and note the important role this value plays in bounding the intersection of all such ideals $I$. We make mention of this intersection in special cases of Stanley-Reisner rings. We conclude with a description of how this work relates to integral closure.

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Thomas M. Ales. 2018-10-13. The $*$-core of the graded maximal ideal in a Stanley-Reisner ring. https://arxiv.org/abs/1810.05896

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