Geodesic
A new characterization of Dedekind domains
Glasgow mathematical journal, Tome 28 (1986) no. 2, pp. 237-239

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this paper all rings are assumed commutative with identity. Among integral domains, Dedekind domains are characterized by the property that every ideal is a product of prime ideals. For a history and proof of this result the reader is referred to Cohen [2, pp. 31–32]. More generally, Mori [5] has shown that a ring has the property that every ideal is a product of prime ideals if and only if it is a finite direct product of Dedekind domains and special principal ideal rings (SPIRS). Rings with this property are called general Z.P.I.-rings. 
Anderson, D. D.; Johnson, E. W. A new characterization of Dedekind domains. Glasgow mathematical journal, Tome 28 (1986) no. 2, pp. 237-239. doi: 10.1017/S0017089500006571
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[1] 1.Butts, H. S. and Gilmer, R. W., Primary ideals and prime power ideals, Canad. J. Math. 18 (1966), 1183–1195. Google Scholar | DOI

[2] 2.Cohen, I. S., Commutative rings with restricted minimum condition, Duke Math. J. 17 (1950), 27–42. Google Scholar | DOI

[3] 3.Gilmer, R. W., Multiplicative Ideal Theory (Marcel Dekker, 1972). Google Scholar

[4] 4.Levitz, K. B., A characterization of general Z.P.I.-rings II, Pacific J. Math. 42 (1972), 147–151. Google Scholar | DOI

[5] 5.Mori, S., Allgemeine Z.P.I.-ringe, J. Sci. Hirosima Univ. Ser. A. 10 (1940), 117–136. Google Scholar

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