Geodesic
Integral ∨-ideals
Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 167-172

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

Let R be an integral domain with quotient field K. A fractional ideal I of R is a ∨-ideal if I is the intersection of all the principal fractional ideals of R which contain I. If I is an integral ∨-ideal, at first one is tempted to think that I is actually just the intersection of the principal integral ideals which contain I.However, this is not true. For example, if R is a Dedekind domain, then all integral ideals are ∨-ideals. Thus a maximal ideal of R is an intersection of principal integral ideals if and only if it is actually principal. Hence, if R is a Dedekind domain, each integral ∨-ideal is an intersection of principal integral ideals precisely when R is a PID. 
Anderson, David F. Integral ∨-ideals. Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 167-172. doi: 10.1017/S0017089500004638
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