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On equimultiplicity

Published online by Cambridge University Press:  24 October 2008

M. Herrmann  and
U. Orbanz
M. Herrmann
Affiliation:
University of Köln
U. Orbanz
Affiliation:
University of Köln
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Extract

This note consists of some investigations about the condition ht(A) = l(A) where A is an ideal in a local ring and l(A) is the analytic spread of A (9).

In (4) we proved the following: If R is a local ring and P a prime ideal such that R/P is regular then (under some technical assumptions) ht(P) = l(P) is equivalent to the equimultiplicity e(R) = e(RP). Also for a general ideal A (which need not be prime), the condition ht(A) = l(A) can be translated into an equality of certain multiplicities (see Theorem 0).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 2 , March 1982 , pp. 207 - 213
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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