Exercise 15, § 2

Let A be a ring. Show that every left A-module E which is flat and finitely presented is projective. (Given a surjective left A-module homomorphism $u : F \to F''$, let $u'$ be the homomorphism

and $\bar{u}$ the homomorphism

where G is a divisible Z-module. Using Exercise 14 first, prove that $\bar{u}$ is injective; then, with a suitable choice for G (Algebra, Chapter 11, §2, Exercise 14), show that $u'$ is surjective.)