Remark 2
Tag 0726, permanent. Cite it as [Bourbaki, Tag 0726].
Algebra, VII, p. 7, § 2. Torsion modules over a principal ideal domain
By the above proof, the projectors of M onto the components are homotheties.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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