Exercise 14, § 2

(a) Generalize Proposition 3 of no. 1 to arbitrary rings.

(b) Let M be an A-module such that, for every multiplicative subset S of A, the kernel of the canonical mapping $M \to S^{-1}M$ is {0} or M. Show that {0} is primary in M (consider for all $a \neq 0$ in A the multiplicative subset of the $a^n$ ($n \geq 0$).