Exercise 8, § 5

Tag 006F, permanent. Cite it as [Bourbaki, Tag 006F].

Algebra, VIII, p. 92

Let A be a principal ideal domain and M an A-module. Prove that the following properties are equivalent:

(i) The A-module M is generating.

(ii) The dual of M is nonzero.

(iii) The module M contains a direct factor submodule isomorphic to $A_s$ .

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