Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-30T20:08:57.684Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the homology of ideals ǵenerated by three elements in local rings

Published online by Cambridge University Press:  24 October 2008

Lindsay Burch
Lindsay Burch
Affiliation:
University of Dundee, Scotland
Get access Rights & Permissions [Opens in a new window]

Extract

In this note, I show that, if Q is a local ring and s an integer, 1 < s < codim Q, then there is an ideal As of Q, generated by three or fewer elements of Q, such that

and that, if Q is not regular, then there is an ideal B of Q, generated by three or fewer elements and of infinite homological dimension over Q.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 949 - 952
Copyright
Copyright © Cambridge Philosophical Society 1968

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)Rees, D.A theorem of homological algebra. Proc. Cambridge Philos. Soc. 52 (1956), 605–616.CrossRefGoogle Scholar