Let be a squarefree monomial ideal of a polynomial algebra over a field minimally generated by
of degree , and a set of monomials of degree . Let be a squarefree monomial ideal generated in degree . Suppose that all squarefree monomials of
of degree are some least common multiples of . If contains all least common multiples of two of of degree then depth
and Stanley's Conjecture holds for .

Key Words: Monomial Ideals, Depth, Stanley depth.

2000 Mathematics Subject Classification: Primary: 13C15;

Secondary: 13F20, 13F55, 13P10.