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Hilbert's function in a semi-lattice

Published online by Cambridge University Press:  24 October 2008

A. Learner
A. Learner
Affiliation:
Trinity CollegeCambridge
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Extract

Samuel (1) introduced a generalized Hilbert function, written Xq(r, a) and defined for arbitrary ideals a in a local ring Q with maximal ideai m. where q is m-primary.

Northcott(2) proved that for a homogeneous ideal ã in a polynomial ring A[X1, …, Xn], where A = Q/q, this is equal to the ordinary Hilbert function χ(r, ã).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 3 , July 1959 , pp. 239 - 243
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

REFERENCES

(1)Samuel, P.La notion de multiplicité en algèbre et en géométrie algébrique. J. Math. pures appl. 30 (1951), 159–275.Google Scholar
(2)Northcott, D. G.Hilbert's function in a local ring. Quart. J. Math. (2), 4 (1953), 67–80.CrossRefGoogle Scholar
(3)Sperner, E.Über einen kombinatorischen Satz von Macauley. Abh. math. Sem. hamburg Univ. 7 (1930), 149–63.CrossRefGoogle Scholar
(4)van der Waerden, B. L.On Hilbert's function, and series of compoaition of ideals. Proc. Kon. Acad. Amsterdam 31 (1928), 749–70.Google Scholar