On the Witt vectors of perfect rings in positive characteristic

Abstract

The purpose of this article is to prove some results on the Witt vectors of perfect $\mathbf{F}_p$-algebras. Let $A$ be a perfect $\mathbf{F}_p$-algebra for a prime integer $p$ and assume that $A$ has the property $\mathbf{P}$. Then does the ring of Witt vectors of $A$ also have $\mathbf{P}$? A main theorem gives an affirmative answer for $\mathbf{P}="\mbox{integrally closed}"$ under a very mild condition.