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Rings associated with ideals and analytic spread

Published online by Cambridge University Press:  24 October 2008

D. Rees
Affiliation:
University of Exeter

Extract

Let A be a Noether ring and let = (a1,…, ar) be an ideal of A. There are a number of graded rings that we can associate with . In this paper we shall be concerned with the following.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Böger, E.Minimalitätsbedingungen in der Theorie der Reductionen Idealen. Schr. Math. Inst. Munster Nr. 40 (1968).Google Scholar
(2)Burch, L.Codimension and analytic spread. Proc. Cambridge Philos. Soc. 72 (1973), 369373.CrossRefGoogle Scholar
(3)Northcott, D. G. and Rees, D.Reductions of ideals in local rings. Proc. Cambridge Philos. Soc. 50 (1954), 145158.CrossRefGoogle Scholar
(4)Ratliff, L. J. JrLocally quasi-unmixed Noetherian rings and ideals of the principal class. Pacific J. Math. 52 (1974), 185205.CrossRefGoogle Scholar
(5)Rees, D.Valuations associated with local rings (I). Proc. London Math. Soc. (3) 5 (1955), 107128.CrossRefGoogle Scholar
(6)Rees, D.Valuations associated with ideals. Proc. London Math. Soc. (3) 6 (1956), 161174.CrossRefGoogle Scholar
(7)Rees, D.Valuations associated with ideals (II). J. London Math. Soc. 31 (1956), 221228.CrossRefGoogle Scholar
(8)Rees, D.Valuations associated with local rings (II). J. London Math. Soc. 31 (1956), 228235.CrossRefGoogle Scholar
(9)Valla, G.Elementi indipendenti rispetto ad un ideale. Rend. Sem. Mat. Univ. Padova 44 (1970), 339354.Google Scholar