Group actions of prime order on local normal rings

Abstract

Let $B$ be a Noetherian normal local ring and $G\subset Aut\left(B\right)$ be a cyclic group of local automorphisms of prime order. Let $A$ be the subring of $G$-invariants of $B$ and assume that $A$ is Noetherian. We prove that $B$ is a monogenous $A$-algebra if and only if the augmentation ideal of $B$ is principal. If in particular $B$ is regular, we prove that $A$ is regular if the augmentation ideal of $B$ is principal.