Geodesic
Noetherian Rings in Which Every Ideal is a Product of Primary Ideals
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 457-459

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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. 
Anderson, D. D. Noetherian Rings in Which Every Ideal is a Product of Primary Ideals. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 457-459. doi: 10.4153/CMB-1980-068-2
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[1] 1. Anderson, D. D., Multiplication ideals, multiplication rings, and the ring R(X), Canad. J. Math. XXVIII (1976), 760-768. Google Scholar

[2] 2. Anderson, D. D., Some remarks on multiplication ideals, (submitted). Google Scholar

[3] 3. Anderson, D. D., Matijevic, J. and Nichols, W., The Krull Intersection Theorem II, Pacific J. Math. 66 (1976), 15-22. Google Scholar

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