The $*$-core of the graded maximal ideal in a Stanley-Reisner ring
We consider ideals $I$ in a Stanley-Reisner ring $k[Δ]$ over the simplical complex $Δ$, such that the tight closure of $I$, $I^*$, is equal to $\mathfrak{m}$, the standard graded maximal ideal of $k[Δ]$. We determine the minimal number of generators of $I$ to be the $\dim Δ+1$ 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.
math.AC↗