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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
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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

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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.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