Stanley decompositions in localized polynomial rings

Details Stanley decompositions in localized polynomial rings Stanley decompositions in localized polynomial rings

2010-05-24

arxiv.org/abs/1005.4254v1

Mathematics

Commutative Algebra

12 pages, 2 figures

Scientific paper

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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