Geodesic
Bezout Domains and Rings with a Distributive Lattice of Right Ideals
Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 286-303

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

It is the purpose of this paper to discuss a construction of right arithmetical (or right D-domains in [5]) domains, i.e., integral domains R for which the lattice of right ideals is distributive (see also [3]). Whereas the commutative rings in this class are precisely the Prüfer domains, not even right and left principal ideal domains are necessarily arithmetical. Among other things we show that a Bezout domain is right arithmetical if and only if all maximal right ideals are two-sided.Any right ideal of a right noetherian, right arithmetical domain is two-sided. This fact makes it possible to describe the semigroup of right ideals in such a ring in a satisfactory way; [3], [5]. 
Brungs, H. H. Bezout Domains and Rings with a Distributive Lattice of Right Ideals. Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 286-303. doi: 10.4153/CJM-1986-014-2
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