Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T13:16:05.379Z Has data issue: false hasContentIssue false
  • English
  • Français

On powers of ideals generated by R-sequences in a Noetherian local ring

Published online by Cambridge University Press:  24 October 2008

A. Caruth
A. Caruth
Affiliation:
Portsmouth Polytechnic
Get access Rights & Permissions [Opens in a new window]

Extract

In a Noetherian commutative ring with identity, every ideal can be expressed (not necessarily uniquely) as a finite intersection of primary ideals (called a primary decomposition). This note is concerned with powers of ideals generated by subsets of an R-sequence in a local ring R (i.e. a Noetherian commutative ring R with identity possessing a unique maximal ideal m) and with a decomposition of such ideals.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 441 - 444
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)Dieudonné, J.On regular sequences. Nagoya Math. J. 27 (1966), 355–356.CrossRefGoogle Scholar
(2)Kaplansky, I.Commutative rings (Allyn and Bacon, 1970).Google Scholar
(3)Kabele, T.Regularity conditions in non-Noetherian rings. Trans. Amer. Math. Soc. 155 (1971), 001–012.CrossRefGoogle Scholar
(4)Northcott, D. G.Ideal theory (Cambridge University Press 1953).CrossRefGoogle Scholar
(5)Serre, J. P.Sur la dimension homologique des anneaux et des modules Noetherian. Proc. of International Symposium, Tokyo-Nikko (1955), pp. 175–189.Google Scholar
(6)Zariski, O. and Samuel, P.Commutative algebra, vol. II (Van Nostrand, 1957).Google Scholar