Geodesic
Convex Directed Subgroups of a Group of Divisibility
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 532-542

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

If D is an integral domain with quotient field K, the group of divisibility G(D) of D is the partially ordered group of non-zero principal fractional ideals with aD ≦ bD if and only if aD contains bD. If K* denotes the multiplicative group of K and U(D) the group of units of D, then G(D) is order isomorphic to K*/U(D), where aU(D) ≦ bU(D) if and only if b/a ∊ D. 
Mott, Joe L. Convex Directed Subgroups of a Group of Divisibility. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 532-542. doi: 10.4153/CJM-1974-049-2
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