Upper bounds for the Stanley depth

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Let I⊂ J be monomial ideals of a polynomial algebra S over a field. Then the Stanley depth of J/I is smaller or equal with the Stanley depth of √J/√I. We give also an upper bound for the Stanley depth of the intersection of two primary monomial ideals Q, Q', which is reached if Q, Q' are irreducible, ht(Q+Q') is odd and √Q, √Q' have no common variable.