The Ratliff–Rush filtration has been shown to be a very useful tool for studying numerical invariants of the ordinary associated graded ring G(I). In this paper, we study some numerical invariants of the associated graded ring to Ratliff–Rush filtration and, as consequence, we prove an upper bound on the first coefficient of the Hilbert polynomial of G which extends classical bounds.
The Hilbert function of the Ratliff-Rush filtration
ROSSI, MARIA EVELINA;VALLA, GIUSEPPE
2005-01-01
Abstract
The Ratliff–Rush filtration has been shown to be a very useful tool for studying numerical invariants of the ordinary associated graded ring G(I). In this paper, we study some numerical invariants of the associated graded ring to Ratliff–Rush filtration and, as consequence, we prove an upper bound on the first coefficient of the Hilbert polynomial of G which extends classical bounds.
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