Definition 3

Tag 00AU, permanent. Cite it as [Bourbaki, Tag 00AU].

Algebra, VIII, p. 161, § 9. Radical

Let A be a ring, and let M be an A-module. A projective cover of M is a pair $(P, u)$ , where P is a projective A-module and $u$ a surjective homomorphism from P to M such that we have $u(P')\not= M$ for every proper A-submodule $P'$ of P.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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