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Two classical theorems of ideal theory

Published online by Cambridge University Press:  24 October 2008

D. Rees
D. Rees
Affiliation:
Downing CollegeCambridge
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Extract

The purpose of this note is to present new proofs of two classical theorems in ideal theory, both due to W. Krull: the intersection theorem (see Krull(1) for the original proof, and Northcott (2), Chapter III, where the theorem is stated in the form proved below), and the principal ideal theorem ((1), or (2), Chapter III, Theorem 6). Both proofs depend on a device introduced by the author in (3) in another connexion.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 1 , January 1956 , pp. 155 - 157
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Krull, W.Primidealketten in allgemeinen Ringbereichen. S. B. Heidelberg. Akad. Wiss. (1928), 7 Abh.Google Scholar
(2)Northcott, D. G.Ideal theory (Camb. Tracts Math. no. 42).Google Scholar
(3)Rees, D.Valuations associated with ideals. II. To appear in J. Lond. math. Soc.Google Scholar