Stanley decompositions in localized polynomial rings

2010/05/24 by Sumiya Nasir, Nasir, Sumiya, Asia Rauf +1
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1005.4254

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⊂ I⊂ 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 \ZZⁿ-graded K-vector spaces.

Citations

• Stanley decompositions and localization

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• Special Stanley Decompositions
• Values and bounds of the Stanley depth
• Size and Stanley depth of monomial ideals
• On the Behaviour of Stanley Depth under Variable Adjunction