Stanley decompositions in localized polynomial rings

الأصل · EN

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 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 ⁿ-graded K-vector spaces.