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A basis theorem for polynomial modules

Published online by Cambridge University Press:  24 October 2008

D. Rees
D. Rees
Affiliation:
Downing CollegeCambridge
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Extract

The purpose of the present note is to prove a basis theorem for polynomial modules (Theorem 1 below). As an application, a proof of the Hilbert function theorem for homogeneous modules (Snapper (1)) is obtained. Both these proofs are elementary in the sense that they do not depend on the decomposition theory for modules over a Noether ring.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 1 , January 1956 , pp. 12 - 16
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Snapper, E.Polynomial matrices …. Amer. J. Math. 69 (1947), 299–326 and 622–52.CrossRefGoogle Scholar
(2)Uzkov, A. I.An algebraic lemma and the normalization theorem of E. Noether. Mat. Sborn. (N.S.), 22 (64) (1948), 349–50 (in Russian)Google Scholar
Uzkov, A. I.Math. Rev. 10 (1949), 97.Google Scholar