Remark

Tag 0E18, permanent. Cite it as [Bourbaki, Tag 0E18].

If $A$ is (commutative) a domain, the preceding conditions are also equivalent to the following :

(iii') : every divisible a-module is injective,

(vi) : every torsion-free a-module is flat and $A$ is noetherian.

Domains satisfying these conditions are called Dedekind rings (cf. X, p. 204, Exercise 12 and AC, VII, § 2, No. 2, Th. 1).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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