Vol. 7, No. 1, 2013

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Group actions of prime order on local normal rings

Franz Kiràly and Werner Lütkebohmert

Vol. 7 (2013), No. 1, 63–74
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.

Keywords
algebraic geometry, commutative algebra, group actions
Primary: 14L30
Secondary: 13A50
Milestones
Received: 14 April 2011
Revised: 23 January 2012
Accepted: 20 February 2012
Published: 28 March 2013
Authors
 Franz Kiràly Berlin Institute of Technology Machine Learning Group Marchstraße 23 10587 Berlin Germany Freie Universität Berlin Discrete Geometry Group Arnimallee 2 14195 Berlin Germany Mathematisches Forschungsinstitut Oberwolfach Schwarzwaldstraße 9-11 77709 Oberwolfach Germany Werner Lütkebohmert Dept. of Pure Mathematics University of Ulm Helmholtzstraße 18 89069 Ulm Germany