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Codimension and analytic spread

Published online by Cambridge University Press:  24 October 2008

Lindsay Burch
Lindsay Burch
Affiliation:
Department of Mathematics, University of Dundee, Nethergate, Dundee, DD1 4HN
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Extract

In this paper, I shall establish the sufficiency of certain conditions on an ideal A of a local ring Q, and on a set {g1 …,gk} of elements of Q generating a proper ideal G, for the ideals A and G to be analytically disjoint. Hence I shall establish an upper bound for the analytic spread of A.

The maximal ideal of Q will be denoted throughout by M, and it will be assumed that the field Q/M is infinite.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 369 - 373
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Northcott, D. G. and Rees, D.Reductions of Ideals in Local Rings. Proc. Cambridge Philos. Soc. 50 (1954), 145–158.Google Scholar
(2)Zariski, O. and Samuel, P.Commutative Algebra, vol. 2 (D. Van Nostrand, 1960).Google Scholar