Exercise 15, § 2

(a) If A is a Priiferian domain, $A/p$ is Priiferian for every prime ideal $p$ of A.

(b) If A is Priiferian, so is $S^{-1}A$ for every multiplicative subset $S$ of A not containing 0.

(c) Let K be a field and $(A_\lambda)$ a non-empty right directed family of subrings of K. Show that, if the $A_\lambda$ are Priiferian domains, so is their union A (use Exercise 12 ($\zeta$)).