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Abstract: We introduce the concept of Stanley decompositions in the localizedpolynomial ring $S f$ where $f$ is a product of variables, and we show that theStanley depth does not decrease upon localization. Furthermore it is shown thatfor monomial ideals $J\subset I\subset S f$ the number of Stanley spaces in aStanley decomposition of $I-J$ is an invariant of $I-J$. For the proof of thisresult we introduce Hilbert series for $\ZZ^n$-graded $K$-vector spaces.



Author: Sumiya Nasir, Asia Rauf

Source: https://arxiv.org/







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