Coefficient ideals

Abstract

Let R be a d-dimensional Noetherian quasi-unmixed local ring with maximal ideal M and an M-primary ideal I with integral closure. We prove that there exist unique largest ideals Ik for 1 ≤ k ≤ d lying between I and such that the first k + 1 Hilbert coefficients of I and Ik coincide. These coefficient ideals clarify some classical results related to. We determine their structure and immediately apply the structure theorem to study the associated primes of the associated graded ring of I.

Document Type

Article

DOI

https://doi.org/10.1090/S0002-9947-1991-1013338-3

Publication Date

1-1-1991

Journal Title

Transactions of the American Mathematical Society

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