Dorin Popescu and Andrei Zarojanu: Depth of some square free monomial ideals, p.117-124


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

Key Words: Monomial Ideals, Depth, Stanley depth.

2000 Mathematics Subject Classification: Primary: 13C15;
Secondary: 13F20, 13F55, 13P10.

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