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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.

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

1. Eagon, J. A. and Northcott, D. G., “Ideals defined by matrices and a certain complex associated with them”, Proc. Roy. Soc., (A), 269 (1962), 188–204.Google Scholar
2. Gröbner, W., Modern Algebraische Geometrie (Springer, 1949).CrossRefGoogle Scholar
3. Nagata, M., “The theory of multiplicity in general local rings”, Proc. Intern. Symposium on Number Theory (Tokyo and Nikko, 1955), 191–225.Google Scholar
4. Salmon, G., Lessons introductory to the modern higher algebra, second edition (Dublin, 1866).Google Scholar
5. Schiffels, G., Graduierte Ringe und Moduln, Bonner Mathematische Schriften, Nr. 11 (Bonn, 1960).Google Scholar
6. Zariski, O. and Samuel, P., Commutative Algebra, Vol. 2 (van Nostrand, 1960).CrossRefGoogle Scholar