Simplicial complexes with rigid depth

Details Simplicial complexes with rigid depth Simplicial complexes with rigid depth

2012-01-16

arxiv.org/abs/1201.3325v1

Mathematics

Commutative Algebra

Scientific paper

We extend a result of Minh and Trung to get criteria for $\depth I=\depth\sqrt{I}$ where $I$ is an unmixed monomial ideal of the polynomial ring $S=K[x_1,..., x_n]$. As an application we characterize all the pure simplicial complexes $\Delta$ which have rigid depth, that is, which satisfy the condition that for every unmixed monomial ideal $I\subset S$ with $\sqrt{I}=I_\Delta$ one has $\depth(I)=\depth(I_\Delta).$

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