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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
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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

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References

REFERENCES

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