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Noetherian Rings in Which Every Ideal is a Product of Primary Ideals

Published online by Cambridge University Press:  20 November 2018

D. D. Anderson
D. D. Anderson*
Affiliation:
The University of Iowa, Iowa City, Iowa 52242
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The classical rings of number theory, Dedekind domains, are characterized by the property that every ideal is a product of prime ideals. More generally, a commutative ring R with identity has the property that every ideal is a product of prime ideals if and only if R is a finite direct sum of Dedekind domains and special principal ideal rings. These rings, called general Z.P.I. rings, are also characterized by the property that every (prime) ideal is finitely generated and locally principal.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 4 , 01 December 1980 , pp. 457 - 459
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Anderson, D. D., Multiplication ideals, multiplication rings, and the ring R(X), Canad. J. Math. XXVIII (1976), 760-768.Google Scholar
2. Anderson, D. D., Some remarks on multiplication ideals, (submitted).Google Scholar
3. Anderson, D. D., Matijevic, J. and Nichols, W., The Krull Intersection Theorem II, Pacific J. Math. 66 (1976), 15-22.Google Scholar