Geodesic
On Divisibility and Injectivity
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 901-919

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

In the category of abelian groups the concepts of divisible group and injective group coincide. In (4) this is generalized to modules over an integral domain and it is proved for a (commutative) integral domain that the concepts of divisible module and injective module coincide if and only if the ring is hereditary if and only if the ring is a Dedekind domain.In (8) the assumption of commutativity is dropped and the ring is assumed to have a one-sided field of quotients. The result obtained is essentially the same as in the commutative case; see the theorem following 6.2. In (13) the requirement that the ring have no zero-divisors is also dropped and the ring is assumed to possess what we have called an Ore ring (see the definition following 6.2). The result obtained is the equivalent of parts (a) and (b) of our 6.13. 
Helzer, Garry. On Divisibility and Injectivity. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 901-919. doi: 10.4153/CJM-1966-091-2
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