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The Hilbert function of the tensor product of two multigraded modules

Published online by Cambridge University Press:  26 February 2010

D. G. Northcott
D. G. Northcott
Affiliation:
The University, Sheffield.
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Extract

The theorem proved in this paper is basic for a general intersection theory applicable to multigraded polynomial rings. When the polynomial ring is graded by the non-negative integers the facts, in one form or another, are well known, but on passing to more general gradings fresh complications appear. These are not wholly trivial and, as the author was unable to find an account of these matters in the literature, it may be of interest if one is given here.

Type
Research Article
Information
Mathematika , Volume 10 , Issue 1 , June 1963 , pp. 43 - 57
Copyright
Copyright © University College London 1963

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References

1. Bourbaki, N., Eléménts de Mathématique, Livre II, Chapitre III (Algèbre Multilinéaire), Actualités Scientifiques et Industrielles, No. 1044 (Hermann, 1948).Google Scholar
2. Schiffels, G., Graduierte Ringe und Moduln, Bonner Math. Schriften, Nr. 11 (1960).Google Scholar
3. Zariski, O. and Samuel, P., Commutative algebra, Vol. 1 (van Nostrand, 1958).Google Scholar