Monomial ideals via square-free monomial ideals

By Sara Faridi. 2005

70 citations recorded by the source corpus.

We study monomial ideals using the operation polarization to first turn them into square-free monomial ideals. We focus on monomial ideals whose polarization produce simplicial trees, and show that many of the properties of simplicial trees hold for such ideals.This includes Cohen-Macaulayness of the Rees ring, and being sequentially Cohen-Macaulay. The appendix is an independent study of primary decomposition in a sequentially Cohen-Macaulay module. We demonstrate how every submodule appearing in the filtration of a sequentially Cohen-Macaulay module can be described in terms of the primary decomposition of the 0-submodule.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1630bcfc9d9ad009598858c020dd500e77e31c1b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Resolutions of square-free monomial ideals via facet ideals: a survey (2006, background): “To learn more about the properties of edge ideals, one should see [1, 2, 6, 16, 17, 25, 26, 27, 36, 38, 39, 40, 41, 44, 46]; further properties of facet ideals can be found in the sequels [12, 13, 14] to Faridi’s paper cited above.”
Embedded Associated Primes of Powers of Square-free Monomial Ideals (2008, result): “In particular, we use a result of Faridi (see Lemma 4.4) which gives a correspondence (which is not necessarily one-to-one) between the associated primes of I t and the associated primes of its polarization.”