Stanley decompositions in localized polynomial rings

• DOI: 10.1007/s00229-010-0414-9
• Publication Date: 2010-11-26T16:26:45Z
• Authors: Sumiya Nasir; Asia Rauf
• Keywords: FOS: Mathematics; 0101 mathematics; Mathematics - Commutative Algebra; Commutative Algebra (math.AC); 01 natural sciences; Primary 13H10, Secondary 13P10, 13C14, 13F20

12 pages, 2 figures<br/>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.<br/>