A -dimensional extension of a lemma of Huneke's and formulas for the Hilbert coefficients

Author:
Sam Huckaba

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1393-1401

MSC (1991):
Primary 13D40, 13A30, 13H10

DOI:
https://doi.org/10.1090/S0002-9939-96-03182-6

MathSciNet review:
1307529

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Abstract | References | Similar Articles | Additional Information

Abstract: A -dimensional version is given of a -dimensional result due to C. Huneke. His result produced a formula relating the length to the difference , where is primary for the maximal ideal of a -dimensional Cohen-Macaulay local ring , is a minimal reduction of , , and is the Hilbert-Samuel polynomial of . We produce a formula that is valid for arbitrary dimension, and then use it to establish some formulas for the Hilbert coefficients of . We also include a characterization, in terms of the Hilbert coefficients of , of the condition .

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Additional Information

**Sam Huckaba**

Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306-3027

Email:
huckaba@math.fsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03182-6

Keywords:
Hilbert-Samuel polynomial,
depth,
associated graded ring,
Cohen-Macaulay

Received by editor(s):
June 8, 1994

Received by editor(s) in revised form:
November 8, 1994

Additional Notes:
The author was partially supported by the NSA (#MDA904-92-H-3040).

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1996
American Mathematical Society