Abstract. Let Q and Q ′ be two monomial primary ideals of a polynomial algebra S over a field. We give an upper bound for the Stanley depth of S/(Q ∩Q ′ ) which is reached if Q,Q ′ are irreducible. Also we show that Stanley’s Conjecture holds for Q1 ∩ Q2, S/(Q1 ∩ Q2 ∩ Q3), (Qi)i being some irreducible monomial ideals of S
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