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arXiv · 1005.4254

Stanley decompositions in localized polynomial rings

Sumiya Nasir·Asia Rauf
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Abstract

We introduce the concept of Stanley decompositions in the localized polynomial ring $S_f$ 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 $J\subset I\subset S_f$ the number of 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 $\ZZ^n$-graded $K$-vector spaces.

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Sumiya Nasir, Asia Rauf. 2010-05-24. Stanley decompositions in localized polynomial rings. https://arxiv.org/abs/1005.4254

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