Three generated, squarefree, monomial ideals

Abstract

Let $I⊋J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\ge d$, resp. $\ge d+1$ . Suppose that $I$ is generated by three monomials of degrees $d$. If the Stanley depth of $I/J$ is $\le d+1$ then the usual depth of $I/J$ is $\le d+1$ too.

To appear in Bulletin Math. Soc. Sci. Math. Roumanie {\bf 58 (106)}, (2015), no 3

References in corpus (7)

• An inequality between depth and Stanley depth
• Special Stanley Decompositions
• Lexsegment ideals of Hilbert depth 1
• The Stanley conjecture on monomial almost complete intersection ideals
• Depth of some square free monomial ideals
• Depth and minimal number of generators of square free monomial ideals
• Depth of some special monomial ideals

Cited by in corpus (3)

• Stanley depth on five generated, squarefree, monomial ideals
• Depth in a pathological case
• Stanley depth of monomial ideals