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A note on the Hilbert functions of certain ideals which are defined by matrices

Published online by Cambridge University Press:  26 February 2010

J. A. Eagon and
D. G. Northcott
J. A. Eagon
Affiliation:
The University, Sheffield
D. G. Northcott
Affiliation:
The University, Sheffield
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Extract

Let I be a homogeneous ideal in the polynomial ring R = Λ[X1, X2, …, XN], where Λ is a field or, more generally, an Artin ring†. Then R|I has an induced structure as a graded R-module and its homogeneous elements of degree n form a Λ-module of finite length. If this length is denoted by H(n, R|I), then H(n, R|I), considered as a function of n, is often known as the Hilbert function of the ideal I although, in other contexts, it is called the Hilbert function of the graded module R|I. We shall adopt the latter terminology.

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Type
Research Article
Information
Mathematika , Volume 9 , Issue 2 , December 1962, pp. 118 - 126
Copyright
Copyright © University College London 1962

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References

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