Depth of factors of square free monomial ideals

Details Depth of factors of square free monomial ideals Depth of factors of square free monomial ideals

2011-10-10

arxiv.org/abs/1110.1963v2

Mathematics

Commutative Algebra

Scientific paper

Let $I$ be an ideal of a polynomial algebra over a field, generated by $r$-square free monomials of degree $d$. If $r$ is bigger (or equal if $I$ is not principal) than the number of square free monomials of $I$ of degree $d+1$ then $\depth_SI= d$. Let $J\subset I$, $J\not =0$ be generated by square free monomials of degree $\geq d+1$. If $r$ is bigger than the number of square free monomials of $I\setminus J$ of degree $d+1$ then $\depth_SI/J= d$. In particular Stanley's Conjecture holds in both cases.

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