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The defect of a one-dimensional local ring

Published online by Cambridge University Press:  26 February 2010

D. Kirby
Affiliation:
The University, Leeds, 2.
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Extract

In a recent paper Northcott [3] introduced the notion of the reduction number of a one-dimensional local ring, and demonstrated its importance in the theory of abstract dilatations. In the present paper we define the reduction number of an ideal which is primary for the maximal ideal of a one-dimensional local ring, and show that under certain necessary and sufficient conditions the reduction numbers can take only a finite number of values.

Type
Research Article
Copyright
Copyright © University College London 1959

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References

1.Northcott, D. G., Ideal Theory (Cambridge, 1953).Google Scholar
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