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

2018/10/13 by Ales, Thomas M.
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.05896

Abstract

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 \mathfrakm, 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.

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