Upper bounds of depth of monomial ideals

preprint2012arXivOpen access

Let $J\subsetneq I$ be two ideals of a polynomial ring $S$ over a field, generated by square free monomials. We show that some inequalities among the numbers of square free monomials of $I\setminus J$ of different degrees give upper bounds of $\depth_SI/J$.

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Upper bounds of depth of monomial ideals

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