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Notes on irreducible ideals

Published online by Cambridge University Press:  17 April 2009

David J. Smith
David J. Smith
Affiliation:
Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand.
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Abstract

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Every ideal of a Noetherian ring may be represented as a finite intersection of primary ideals. Each primary ideal may be decomposed as an irredundant intersection of irreducible ideals. It is shown that in the case that Q is an M-primary ideal of a local ring (R, M) satisfying the condition that Q: M = Q + Ms−1 where s is the index of Q, then all irreducible components of Q have index s. (Q is “index-unmixed”.) This condition is shown to hold in the case that Q is a power of the maximal ideal of a regular local ring, and also in other cases as illustrated by examples.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 3 , June 1985 , pp. 321 - 324
Copyright
Copyright © Australian Mathematical Society 1985

References

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