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Upper bounds of Hilbert coefficients and Hilbert functions

Published online by Cambridge University Press:  01 July 2008

JUAN ELIAS
JUAN ELIAS*
Affiliation:
Departament d'Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain. e-mail: [email protected]
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Abstract

Let (R, m) be a d-dimensional Cohen–Macaulay local ring. In this paper we prove, in a very elementary way, an upper bound of the first normalized Hilbert coefficient of a m-primary ideal I ⊂ R that improves all known upper bounds unless for a finite number of cases, see Remark 2.3. We also provide new upper bounds of the Hilbert functions of I extending the known bounds for the maximal ideal.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 87 - 94
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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