Prime filtrations of monomial ideals and polarizations

2006/05/04 by Jahan, Ali Soleyman · 1 citation
#13A02 #13D02 #13D40 #13P10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0605119

Abstract

We show that all monomial ideals in the polynomial ring in at most 3 variables are pretty clean and that an arbitrary monomial ideal I is pretty clean if and only if its polarization I^p is clean. This yields a new characterization of pretty clean monomial ideals in terms of the arithmetic degree, and it also implies that a multicomplex is shellable if and only the simplicial complex corresponding to its polarization is (non-pure) shellable. We also discuss Stanley decompositions in relation to prime filtrations.

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• Betti numbers and almost complete intersection monomial ideals

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