Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-11T04:05:30.421Z Has data issue: false hasContentIssue false
  • English
  • Français

The reduction number of a one-dimensional local ring

Published online by Cambridge University Press:  26 February 2010

D. G. Northcott
D. G. Northcott
Affiliation:
The University, Sheffield.
Get access

Extract

In the present paper we consider a one-dimensional local ring Q with maximal ideal tn and residue field K = Q/m. It will be assumed that not every element of mis a zero-divisor but no other restricting hypothesis will be made. In particular Q and K may have unequal characteristics and K may be finite.

Type
Research Article
Information
Mathematika , Volume 6 , Issue 2 , December 1959 , pp. 87 - 90
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.)

References

1.Cohen, I. S., “On the structure and ideal theory of complete local rings“, Trans. American Math. Soc., 59 (1946), 54–106.CrossRefGoogle Scholar
2.Northcott, D. G., “Hilbert's function in a local ring’, Quart. J. of Math. (Oxford) (2), 4 (1953), 67–80.CrossRefGoogle Scholar
3.Northcott, D. G., “On the notion of a first neighbourhood ring with an application to the AF+BΦ theorem”, Proc. Cambridge Phil. Soc., 53 (1956), 43–56.Google Scholar
4.Northcott, D. G., “Some contributions to the theory of one-dimensional local rings“, Proc. London Math. Soc. (3), 8 (1958), 388–415.CrossRefGoogle Scholar
5.Northcott, D. G., “An algebraic relation connected with the theory of curves on non-singular surfaces“, J. London Math. Soc., 34 (1959), 195–204.CrossRefGoogle Scholar
6.Samuel, P., Algèbre locale, Mem. Sci. Math., 123 (Paris, 1953).Google Scholar