Corollary 1
Tag 0736, permanent. Cite it as [Bourbaki, Tag 0736].
Algebra, chapter VII, § 3. Free modules over a principal ideal domain
— If every left ideal of is projective, then every submodule of a projective left -module is projective.
Indeed every projective -module is a submodule of a free -module (II, p. 231, Prop. 4), and Th. 1 applies.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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