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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Coefficient ideals


Author: Kishor Shah
Journal: Trans. Amer. Math. Soc. 327 (1991), 373-384
MSC: Primary 13D40; Secondary 13A30, 13H15
MathSciNet review: 1013338
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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 $ \overline I $. We prove that there exist unique largest ideals $ {I_k}$ for $ 1 \leq k \leq d$ lying between $ I$ and $ \overline I $ such that the first $ k + 1$ Hilbert coefficients of $ I$ and $ {I_k}$ coincide. These coefficient ideals clarify some classical results related to $ \overline I $. We determine their structure and immediately apply the structure theorem to study the associated primes of the associated graded ring of $ I$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1013338-3
PII: S 0002-9947(1991)1013338-3
Article copyright: © Copyright 1991 American Mathematical Society