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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)
Received August 19, 2009; Revised October 1, 2009
Abstract
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It is known that if
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. |
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Keywords and phrases:
Hilbert polynomial, Hilbert function, Ratliff-Rush closure, integral closure. |
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