Let *I ⊋ J* be two squarefree monomial ideals of a polynomial algebra over a field. Suppose that is generated by one squarefree monomial of degree , and other squarefree monomials of degrees . If the Stanley depth of is then almost always the usual depth of is too.

Key Words: Monomial Ideals, Depth, Stanley depth.

2000 Mathematics Subject Classification: Primary: 13C15;

Secondary: 13F20, 13F55, 13P10.

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