Exercise 5, § 1

Let $A$ be a ring of characteristic $p$. a) The ring $W(A)$ is an integral domain if and only if $A$ is an integral domain. b) $W(A)$ is reduced if and only if $A$ is reduced. c) The following conditions are equivalent: (i) $A$ is a perfect ring of characteristic $p$. (ii) $W(A)/pW(A)$ is reduced.

EXERCISES

AC IX.43