Hostname: page-component-7b7567c8c-mnklg Total loading time: 0 Render date: 2026-11-13T11:23:45.208Z Has data issue: false hasContentIssue false
  • English
  • Français

The defect of a one-dimensional local ring

Published online by Cambridge University Press:  26 February 2010

D. Kirby
D. Kirby
Affiliation:
The University, Leeds, 2.
Get access

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.

Information

Type
Research Article
Information
Mathematika , Volume 6 , Issue 2 , December 1959, pp. 91 - 97
Copyright
Copyright © University College London 1959

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Northcott, D. G., Ideal Theory (Cambridge, 1953).Google Scholar
2.Northcott, D. G., “A general theory of one-dimensional local rings”, Proc. Glasgow Math. Soc., 2 (1956), 159–169.Google Scholar
3.Northcott, D. G., “The reduction number of a one-dimensional local ring”, Mathematika, 6 (1959), 87–90.Google Scholar
4.Northcott, D. G., and Rees, D., “A note on reductions of ideals with an application to the generalized Hilbert function”, Proc. Cambridge Phil. Soc., 50 (1954), 353–359.Google Scholar
5.Rees, D., “Two classical theorems of ideal theory”, Proc. Cambridge Phil. Soc., 52 (1956), 155–157.Google Scholar
6.Samuel, P., Algèbre Locale, Mém. Sci. Math., 123 (Paris, 1953).Google Scholar