Exercise 1, § 4

Show that in the statement of Proposition 2, condition (a) can be replaced by: (a') $\operatorname{Tor}_1^R(\rho_*(E), F) = 0$ for every monogenous right $S$-module $E$. (To prove that (a') implies (a), consider first the case when $E$ is generated by $n$ elements and argue by induction on $n$.)