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We give different bounds for the Stanley depth of a monomial ideal $I$ of apolynomial algebra $S$ over a field $K$. For example we show that the Stanleydepth of $I$ is less or equal with the Stanley depth of any prime idealassociated to $S/I$. Also we show that the Stanley conjecture holds for $I$ and$S/I$ when the associated prime ideals of $S/I$ are generated by disjoint setsof variables.

Values and bounds of the Stanley depth