Stanley decompositions in localized polynomial rings
Dr. Asia Rauf
Let K be a field, S=K[x1,... ,xn] be the polynomial ring in n variables over K. We introduce the concept of Stanley decompositions in the localized polynomial ring Sf where f is a product of variables, and we show that the Stanley depth does not decrease upon localization. Furthermore it is shown that for monomial ideals J ⊂ I ⊂ Sf the number of maximal Stanley spaces in a Stanley decomposition of I /J is an invariant of I /J. For the proof of this result we introduce Hilbert series for multigraded K-vector spaces.
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