Geodesic
An Essential Ring Which is Not A v-Multiplication Ring
Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 856-861

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

An integral domain D is called an essential ring if D = ∩αVα where the Vα are valuation rings which are quotient rings of D. D is called a v-multiplication ring if the finite divisorial ideals of D form a group. Griffin [2, pp. 717-718] has observed that every v-multiplication ring is essential and that an essential ring having a defining family of valuation rings {Vα} which is of finite character (i.e. every nonzero element of D is a non-unit in at most finitely many Vα) is necessarily a v-multiplication ring; but he conjectures that, in general, there exists an essential ring which is not a v-multiplication ring. 
Heinzer, William; Ohm, Jack. An Essential Ring Which is Not A v-Multiplication Ring. Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 856-861. doi: 10.4153/CJM-1973-088-5
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[1] 1. Bourbaki, N., Algebre commutative, Chapters 5, 6, 7 (Hermann, Paris, 1964/65). Google Scholar

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[4] 4. Heinzer, W. and Ohm, J., Noetherian intersections of integral domains, Trans. Amer. Math. Soc. 167 (1972), 291–308. Google Scholar

[5] 5. Jaffard, P., Les systèmes d'idéaux (Dunod, Paris, 1960). Google Scholar

[6] 6. Ohm, J., Semivaluations and groups of divisibility, Can. J. Math. 21 (1969), 576–591. Google Scholar

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