Monomial ideals via square-free monomial ideals

Details Monomial ideals via square-free monomial ideals Monomial ideals via square-free monomial ideals

2005-07-12

arxiv.org/abs/math/0507238v1

Mathematics

Commutative Algebra

Scientific paper

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.

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