Depth of some square free monomial ideals

Abstract

Let $I⊋J$ be two square free monomial ideals of a polynomial algebra over a field generated in degree $\ge 1$, resp. $\ge 2$ . Almost always when $I$ contains precisely one variable, the other generators having degrees $\ge 2$, if the Stanley depth of $I/J$ is $\le 2$ then the usual depth of $I/J$ is $\le 2$ too, that is the Stanley Conjecture holds in these cases.

submitted to Bull. Math. Soc. Sci. Math. Roumanie

References in corpus (2)

• Special Stanley Decompositions
• Lexsegment ideals of Hilbert depth 1