Exercise 12, § 3

Soit $c$ an infinite cardinal. Suppose that every left ideal of the ring $A$ admits a generating set of cardinal $\leqslant c$. Now prove that every $A$-module generated by a set of elements of cardinal $\leqslant c$ admits a left resolution by free $A$-modules of rank $\leqslant c$ (cf. VIII, § 1, exercise 13).