Category: List of Bases 2011 Throughout the year  RESEARCH IN MATHEMATICS 

Title:

Stanley decompositions in localized polynomial rings

Start Time:

14:30

Location:

ICTP (Leonardo da Vinci Building Luigi Stasi Seminar Room)

Contact:

Mabilo

Speaker(s):

Dr. Asia Rauf (ICTP)

Description:

Abstract:
Let K be a field, S=K[x1,... ,xn] be the polynomial ring in n variables over K. 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 maximal 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 multigraded K-vector spaces.