Skip to main content Accessibility help
×
Home
Hostname: page-component-544b6db54f-fg2fv Total loading time: 0.216 Render date: 2021-10-23T22:11:14.128Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

On a class of commutative Noetherian rings

Published online by Cambridge University Press:  24 October 2008

Lindsay Burch
Affiliation:
Department of Mathematics, University of Dundee, Nethergate, Dundee, DD1 4HN

Extract

If A, B are ideals of a commutative ring R, such that BA, 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
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

(1)Northcott, D. G. and Rees, D.Reductions of ideals in local rings. Proc. Cambridge Philos. Soc. 50 (1954), 145158.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), 941948.CrossRefGoogle Scholar
1
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

On a class of commutative Noetherian rings
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

On a class of commutative Noetherian rings
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

On a class of commutative Noetherian rings
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *