On coefficient ideals

Let be a Cohen-Macaulay local ring of dimension with infinite residue field and let I be an primary ideal. Let For let be the ith-coefficient ideal of I. Also let denote the Ratliff-Rush closure of A. Let be the associated graded ring of I. We show that if for then for all . In particular if G is ge...

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Bibliographic Details
Published in:Communications in algebra 2023-12, Vol.51 (12), p.4967-4975
Main Author: Puthenpurakal, Tony J.
Format: Article
Language:English
Subjects:
Associated graded rings
coefficient ideals
Hilbert polynomial
multiplicity
reduction
Secondary: 13H10
Citations: Items that this one cites
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Summary:Let be a Cohen-Macaulay local ring of dimension with infinite residue field and let I be an primary ideal. Let For let be the ith-coefficient ideal of I. Also let denote the Ratliff-Rush closure of A. Let be the associated graded ring of I. We show that if for then for all . In particular if G is generalized Cohen-Macaulay then for all . As a consequence we get that if A is an analytically unramified domain with G generalized Cohen-Macaulay, then the -ification of the Rees algebra A[It] is .
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2023.2223305