Graph and depth of a monomial squarefree ideal

Details Graph and depth of a monomial squarefree ideal Graph and depth of a monomial squarefree ideal

2011-04-29

arxiv.org/abs/1104.5596v2

Mathematics

Commutative Algebra

Scientific paper

Let $I$ be a monomial squarefree ideal of a polynomial ring $S$ over a field $K$ such that the sum of every three different of its minimal prime ideals is the maximal ideal of $S$, or more general a constant ideal. We associate to $I$ a graph on $[s]$, $s=|\Min S/I|$ on which we may {\em read} the depth of $I$. In particular, $\depth_S\ I$ does not depend of char $K$. Also we show that $I$ satisfies the Stanley's Conjecture.

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