Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T01:19:27.868Z Has data issue: false hasContentIssue false
  • English
  • Français

On a class of commutative Noetherian rings

Published online by Cambridge University Press:  24 October 2008

Lindsay Burch
Lindsay Burch
Affiliation:
Department of Mathematics, University of Dundee, Nethergate, Dundee, DD1 4HN
Get access Rights & Permissions [Opens in a new window]

Extract

If A, B are ideals of a commutative ring R, such that B ⊆ A, and, for some positive integer r, Ar = BAr−1 then B is said to be a reduction of A. (This concept was defined and developed by Northcott and Rees in (1).) In this paper, I shall consider commutative Noetherian rings with the property that no non-zero principal ideal is a reduction of an ideal properly containing it.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 2 , March 1973 , pp. 283 - 287
Copyright
Copyright © Cambridge Philosophical Society 1973

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

REFERENCES

(1)Northcott, D. G. and Rees, D.Reductions of ideals in local rings. Proc. Cambridge Philos. Soc. 50 (1954), 145–158.CrossRefGoogle Scholar
(2)Zariski, O. and Samuel, P.Commutative Algebra, vol. I (D. Van Nostrand, 1958).Google Scholar
(3)Burch, L.On ideals of finite homological dimension in local rings. Proc. Cambridge Philos. Soc. 64 (1968), 941–948.CrossRefGoogle Scholar