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Hilbert's function in a semi-lattice
Published online by Cambridge University Press: 24 October 2008
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