Depth of some special monomial ideals

Abstract

Let $I⊋J$ be two squarefree monomial ideals of a polynomial algebra over a field. Suppose that $I$ is generated by one squarefree monomial of degree $d>0$, and other squarefree monomials of degrees $\ge d+1$. If the Stanley depth of $I/J$ is $\le d+1$ then almost always the usual depth of $I/J$ is $\le d+1$ too.

to appear in Bull. Math. Soc. Sci. Math. Roumanie, {\bf 56(104)}, 2013

References in corpus (3)

• Lexsegment ideals of Hilbert depth 1
• Depth of some square free monomial ideals
• Depth and minimal number of generators of square free monomial ideals

Cited by in corpus (3)

• Three generated, squarefree, monomial ideals
• Stanley depth on five generated, squarefree, monomial ideals
• Stanley depth of monomial ideals