Upper bounds for the Stanley depth

Abstract

Let $I\subset J$ be monomial ideals of a polynomial algebra $S$ over a field. Then the Stanley depth of $J/I$ is smaller or equal with the Stanley depth of $\sqrt{J}/\sqrt{I}$. We give also an upper bound for the Stanley depth of the intersection of two primary monomial ideals $Q$, $Q^{\prime }$, which is reached if $Q$, $Q^{\prime }$ are irreducible, ht$(Q+Q^{\prime })$ is odd and $\sqrt{Q}$, $\sqrt{Q^{\prime }}$ have no common variable.

References in corpus (1)

• On the Stanley Depth of Squarefree Veronese Ideals

Cited by in corpus (2)

• On the Behaviour of Stanley Depth under Variable Adjunction
• Stanley depth of edge ideals