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.
Shah, Kishor. "Coefficient ideals." Transactions of the American Mathematical Society 327, no. 1 (1991): 373-384.
Transactions of the American Mathematical Society