Exercise 9, § 3

Let $\rho : A \to B$ be a ring homomorphism, $M$ an $A$-module. a) If $B$ is a flat right $A$-module and if $M$ admits a finite $n$-presentation, the $B$-module $B \otimes_A M$ admits a finite $n$-presentation. b) If $B$ is a faithfully flat right $A$-module ($X$, p. 169, Exercise 9), and if the $B$-module $B \otimes_A M$ admits a finite $n$-presentation, then $M$ admits a finite $n$-presentation (use Exercise 6, b) and Exercise 12, p. 169).