Dorin Popescu: Stanley depth on five generated, squarefree, monomial ideals , p.75-99

Abstract:

Let I⊋J be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by four squarefree monomials of degrees $d$ and others of degrees $\geq d+1$, or by five special monomials of degrees $d$. If the Stanley depth of $I/J$ is $\leq d+1$ then the usual depth of $I/J$ is $\leq d+1$ too.

Key Words: Monomial Ideals, Depth, Stanley depth.

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

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