Dorin Popescu and Andrei Zarojanu: Depth of some special monomial ideals, p.365-368

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 $\geq d+1$. If the Stanley depth of $I/J$ is $\leq d+1$ then almost always 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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