Commutative Algebra with a View Toward Algebraic Geometry
《Commutative Algebra with a View Toward Algebraic Geometry》 · 第 136 页 · Chapter 4，Exercise 4.11(b)
A finitely presented module $M$ is projective if and only if $M$ is locally free in the sense that the localization $M_P$ is free over $R_P$ for every maximal ideal $P$ of $R$.