JP Journal of Algebra, Number Theory and Applications
Volume 15, Issue 2, Pages 157 - 162
(December 2009)
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A NOTE ON THE EQUALITY OF THE HILBERT POLYNOMIAL AND FUNCTION OF A MODULE WITH RESPECT TO AN IDEAL
Cornelia Naude (South Africa)
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is a 2-dimensional Cohen-Macaulay
local ring with infinite residue field and if I
is a primary ideal which is equal to its Ratliff-Rush closure, then
for all
under certain conditions.
In this paper,
this result
is generalised to the Hilbert polynomial and Hilbert function of a module
M with respect to an ideal I.
A result on the independence of the reduction number is also proved.